Chemistry

Chemistry: The Central Science | 13th Edition | ISBN: 9780321910417 | Authors: Theodore E. Brown; H. Eugene LeMay; Bruce E. Bursten; Catherine Murphy; Patrick Woodward; Matthew E. Stoltzfus
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Author: Theodore E. Brown; H. Eugene LeMay; Bruce E. Bursten; Catherine Murphy; Patrick Woodward; Matthew E. Stoltzfus
Publisher: Pearson
ISBN: 9780321910417
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Chapter: Problem: 79E

Chemistry: The Central Science 13
Many-Electron Atoms and Electron Configurations (Sections) What is wrong with the following electron configurations for atoms in their ground states? (a) (b) (c) .

Chapter: Problem: 80E

Chemistry: The Central Science 13
Many-Electron Atoms and Electron Configurations (Sections) The following electron configurations represent excited states. Identify the element and write its ground-state condensed electron configuration, (a) , (b) (c)

Chapter: Problem: 81AE

Chemistry: The Central Science 13
Consider the two waves shown here, which we will consider to represent two electromagnetic radiations: (a) What is the wavelength of wave \(A\)? Of wave \(B\)? (b) What is the frequency of wave\(A\)? Of wave\(B\)? (c) Identify the regions of the electromagnetic spectrum to which waves \(A

Chapter: Problem: 82AE

Chemistry: The Central Science 13
If you put 120 volts of electricity through a pickle, the pickle will smoke and start glowing orange-yellow. The light is emitted because sodium ions in the pickle become excited; their return to the ground state results in light emission, (a) The wavelength of this emitted light is 589 nm. Calculate

Chapter: Problem: 84AE

Chemistry: The Central Science 13
In August 2011, the Juno spacecraft was launched from Earth with the mission of orbiting Jupiter in 2016. The closest distance between Jupiter and Earth is 391 million miles, (a) If it takes 5.0 years for Juno to reach Jupiter, what is its average speed in mi/hr over this period? (b) Once Juno reache

Chapter: Problem: 83AE

Chemistry: The Central Science 13
Certain elements emit light of a specific wavelength when they are burned. Historically, chemists used such emission wavelengths to determine whether specific elements were present in a sample. Characteristic wavelengths for some of the elements are given in the following table: (a) Determine

Chapter: Problem: 87AE

Chemistry: The Central Science 13
Carotenoids are yellow, orange, and red pigments synthesized by plants. The observed color of an object is not the color of light it absorbs but rather the complementary color, as described by a color wheel such as the one shown here. On this wheel, complementary colors are across from each other.

Chapter: Problem: 85AE

Chemistry: The Central Science 13
(a) Consider the lattice energies for the following compounds: , 3205 kJ/mol; , 2791 kJ/mol; , 2410 kJ/mol; , 2250 kJ/mol; , 2121 kJ/mol. Plot lattice energy versus cation radius for these compounds. If you draw a line through your points, is the slope negative or positive? Explain. (b) Th

Chapter: Problem: 86AE

Chemistry: The Central Science 13
How many elements in the periodic table are represented by a Lewis symbol with a single dot? Which groups are they in?

Chapter: Problem: 88AE

Chemistry: The Central Science 13
In an experiment to study the photoelectric effect, a scientist measures the kinetic energy of ejected electrons as a function of the frequency of radiation hitting a metal surface. She obtains the following plot. The point labeled \(" v_{0} " \) corresponds to light with a wavelength of \(542 \math

Chapter: Problem: 89AE

Chemistry: The Central Science 13
Consider a transition in which the hydrogen atom is excited from \(n=1 \text { to } n=\infty\). (a) What is the end result of this transition? (b) What is the wavelength of light that must be absorbed to accomplish this process? (c) What will occur if light with a shorter wavelength than that

Chapter: Problem: 90AE

Chemistry: The Central Science 13
The human retina has three types of receptor cones, each sensitive to a different range of wavelengths of visible light, as shown in this figure (the colors are merely to differentiate the three curves from one another; they do not indicate the actual colors represented by each curve): (a) E

Chapter: Problem: 91AE

Chemistry: The Central Science 13
Construct a BornHaber cycle for the formation of the hypothetical compound NaCl2, where the sodium ion has a 2+ charge (the second ionization energy for sodium is given in Table 7.2). (a) How large would the lattice energy need to be for the formation of NaCl2 to be exothermic? (b) If we were to esti

Chapter: Problem: 92AE

Chemistry: The Central Science 13
When the spectrum of light from the Sun is examined in high resolution in an experiment similar to that illustrated in Figure 6.9, dark lines are evident. These are called Fraunhofer lines, after the scientist who studied them extensively in the early nineteenth century. Altogether, about 25,000 line

Chapter: Problem: 93AE

Chemistry: The Central Science 13
From the ionic radii given in Figure , calculate the potential energy of a and ion pair that is just touching (the magnitude of the electronic charge is given on the back-inside cover). Calculate the energy of a mole of such pairs. How does this value compare with the lattice energy of (Ta

Chapter: Problem: 96AE

Chemistry: The Central Science 13
Problem 96AE In the television series Star TreK, the transporter beam is a device used to beam down" people from the Starship Enterprise to another location, such as the surface of a planet. The writers of the show put a "Heisenberg compensator" into the transporter beam mechanism. Explain why such

Chapter: Problem: 94AE

Chemistry: The Central Science 13
Bohrs model can be used for hydrogen-like ionsions that have only one electron, such as \(\mathrm{He}^{+} \text {and } \mathrm{Li}^{2+}\) (a) Why is the Bohr model applicable to \(\mathrm{He}^{+}\) ions but not to neutral He atoms? (b) The ground-state energies of \(\mathrm{H}, \mathrm{He

Chapter: Problem: 95AE

Chemistry: The Central Science 13
An electron is accelerated through an electric potential to a kinetic energy of 13.4 keV. What is its characteristic wavelength? [Hint: Recall that the kinetic energy of a moving object is , where m is the mass of the object and v is the speed of the object ]

Chapter: Problem: 98AE

Chemistry: The Central Science 13
Consider the discussion of radial probability functions in A Closer Look in Section 6.6. (a) What is the difference between the probability density as a function of \(r\) and the radial probability function as a function of \(r\)? (b) What is the significance of the term \(4 \pi r^{2}\) in

Chapter: Problem: 97AE

Chemistry: The Central Science 13
Problem 97AE As discussed in the A Closer Look box on Measurement and the Uncertainty Principle," the essence of the uncertainty principle is that we can't make a measurement without disturbing the system that we are measuring, (a) Why can't we measure the position of a subatomic particle without d

Chapter: Problem: 100AE

Chemistry: The Central Science 13
The Chemistry and Life box in Section 6.7 described the techniques called \(NMR and MRI\). (a) Instruments for obtaining \(MRI\) data are typically labeled with a frequency, such as \(600 \mathrm{MHz}\). Why do you suppose this label is relevant to the experiment? (b) What is the value of

Chapter: Problem: 101AE

Chemistry: The Central Science 13
Suppose that the spin quantum number, ms, could have three allowed values instead of two. How would this affect the number of elements in the first four rows of the periodic table?

Chapter: Problem: 99AE

Chemistry: The Central Science 13
For orbitals that are symmetric but not spherical, the contour representations (as in Figures 6.23 and 6.24) suggest where nodal planes exist (that is, where the electron density is zero). For example, the \(p_{x}\) orbital has a node wherever \(x=0\). This equation is satisfied by all points on the

Chapter: Problem: 102AE

Chemistry: The Central Science 13
Problem 102AE Using the periodic table as a guide, write the condensed electron configuration and determine the number of unpaired electrons for the ground state of (a) Br, (b) Ga, (c) Hf, (d) Sb. (e) Bi. (f) Sg.

Chapter: Problem: 103AE

Chemistry: The Central Science 13
Scientists have speculated that element 126 might have a moderate stability, allowing it to be synthesized and characterized. Predict what the condensed electron configuration of this element might be.

Chapter: Problem: 106IE

Chemistry: The Central Science 13
Problem 106IE The stratospheric ozone (03) layer helps to protect us from harmful ultraviolet radiation. It does so by absorbing ultraviolet light and falling apart into an 02 molecule and an oxygen atom, a process Known as photodissociation. 03(g)-02(g) + 0(g) Use the data in Appendix C to cal

Chapter: Problem: 104AE

Chemistry: The Central Science 13
In the experiment shown schematically below, a beam of neutral atoms is passed through a magnetic field. Atoms that have unpaired electrons are deflected in different directions in the magnetic field depending on the value of the electron spin quantum number. In the experiment illustrated, we envisio

Chapter: Problem: 105IE

Chemistry: The Central Science 13
Problem 105IE Microwave ovens use microwave radiation to heat food. The energy of the microwaves is absorbed by water molecules in food and then transferred to other components of the food, (a) Suppose that the microwave radiation has a wavelength of 11.2 cm. How many photons are required to heat 2

Chapter: Problem: 107IE

Chemistry: The Central Science 13
Problem 107IE The discovery of hafnium, element number 72. provided a controversial episode in chemistry. G. Urbain. a French chemist, claimed in 1911 to have isolated an element number 72 from a sample of rare earth (elements 58-71) compounds. However. Niels Bohr believed that hafnium was more l

Chapter: Problem: 108IE

Chemistry: The Central Science 13
(a) Account for formation of the following series of oxides in terms of the electron configurations of the elements and the discussion of ionic compounds in Section 2.7: \(\mathrm{K}_{2} \mathrm{O}, \mathrm{CaO}, \mathrm{Sc}_{2} \mathrm{O}_{3}, \mathrm{TiO}_{2}, \mathrm{~V}_{2} \mathrm{O}_{5}, \

Chapter: Problem: 109IE

Chemistry: The Central Science 13
The first 25 years of the twentieth century were momentous for the rapid pace of change in scientists' understanding of the nature of matter, (a) How did Rutherfords experiments on the scattering of particles by a gold foil set the stage for Bohr's theory of the hydrogen atom? (b) In what ways is de

Chapter: Problem: 110IE

Chemistry: The Central Science 13
The two most common isotopes of uranium are \({ }^{235} \mathrm{U} \mathrm{and}^{238} \mathrm{U}\) (a) Compare the number of protons, the number of electrons, and the number of neutrons in atoms of these two isotopes. (b) Using the periodic table in the front-inside cover, write the electron

Chapter: Problem: 59E

Chemistry: The Central Science 13
Problem 59E Quantum Mechanics and Atomic Orbitals (Sections) A certain orbital of the hydrogen atom has n = 4 and / = 2. (a) What are the possible values of ml for this orbital? (b) What are the possible values of ms for the orbital?

Chapter: Problem: 1E

Chemistry: The Central Science 13
Visualizing Concepts Consider the water wave shown here. (a) How could you measure the speed of this wave? (b) How would you determine the wavelength of the wave? (c) Given the speed and wavelength of the wave, how could you determine the frequency of the wave? (d) Suggest an independent experiment

Chapter: Problem: 1DE

Chemistry: The Central Science 13
Problem 1DE In this chapter, we have learned about the photoelectric effect and its impact on the formulation of light as photons. We have also seen that some anomalous electron configurations of the elements are particularly favorable if each atom has one or more half-filled shell, such as the cas

Chapter: Problem: 2E

Chemistry: The Central Science 13
Visualizing Concepts A popular kitchen appliance produces electromagnetic radiation with a frequency of \(2450 \mathrm{MHz}\) With reference to Figure 6.4, answer the following: (a) Estimate the wavelength of this radiation. (b) Would the radiation produced by the appliance be visible to the human

Chapter: Problem: 4E

Chemistry: The Central Science 13
Problem 4E Visualizing Concepts As shown in the accompanying photograph, an electric stove burner on its highest setting exhibits an orange glow, (a) When the burner setting is changed to low, the burner continues to produce heat but the orange glow disappears. How can this observation be explained

Chapter: Problem: 3E

Chemistry: The Central Science 13
Visualizing Concepts The following diagrams represent two electromagnetic waves. Which wave corresponds to the higher-energy radiation? [Section 6.2]

Chapter: Problem: 5E

Chemistry: The Central Science 13
Problem 5E Visualizing Concepts Stars do not all have the same temperature. The color of light emitted by stars is characteristic of the light emitted by hot objects. Telescopic photos of three stars are shown below: (i) the Sun. which is classified as a yellow star, (ii) Rigel, in the constellatio

Chapter: Problem: 6E

Chemistry: The Central Science 13
Visualizing Concepts The familiar phenomenon of a rainbow results from the diffraction of sunlight through raindrops. (a) Does the wavelength of light increase or decrease as we proceed outward from the innermost band of the rainbow? (b) Does the frequency of light increase or decrease as we procee

Chapter: Problem: 7E

Chemistry: The Central Science 13
Visualizing Concepts A certain quantum mechanical system has the energy levels shown in the accompanying diagram. The energy levels are indexed by a single quantum number \(n\) that is an integer. (a) As drawn, which quantum numbers are involved in the transition that requires the most energy? (b)

Chapter: Problem: 8E

Chemistry: The Central Science 13
Visualizing Concepts Consider a fictitious one-dimensional system with one electron. The wave function for the electron, drawn below, is \(\psi(x)=\sin x \text { from } x=0 \text { to } x=2 \pi\) (a) Sketch the probability density, \(\psi^{2}(x), \text { from } x=0 \text { to } x=2 \pi\) (b) At

Chapter: Problem: 10E

Chemistry: The Central Science 13
Visualizing Concepts The accompanying drawing shows the shape of \(ad\) orbital. (a) Based on the shape, how many of the d orbitals could it be? (b) Which of the following would you need to determine which of the d orbitals it is: (i) the direction of the \(z-\text { axis }\), (ii) the identity of

Chapter: Problem: 9E

Chemistry: The Central Science 13
Visualizing Concepts The contour representation of one of the orbitals for the \(n=3\) shell of a hydrogen atom is shown as follows. (a) What is the quantum number l for this orbital? (b) How do we label this orbital? (c) In which of the following ways would you modify this sketch to show the an

Chapter: Problem: 11E

Chemistry: The Central Science 13
Visualizing Concepts The accompanying drawing shows part of the orbital diagram for an element. (a) As drawn, the drawing is incorrect. Why? (b) How would you correct the drawing without changing the number of electrons? (c) To which group in the periodic table does the element belong? [Section 6.8

Chapter: Problem: 12E

Chemistry: The Central Science 13
Visualizing Concepts State where in the periodic table these elements appear: (a) elements with the valence-shell electron configuration \(n s^{2} n p^{5}\) (b) elements that have three unpaired \(p\) electrons (c) an element whose valence electrons are \(4 s^{2} 4 p^{1}\) (d) the \(d-\text {

Chapter: Problem: 14E

Chemistry: The Central Science 13
Problem 14E The Wave Nature of Light (Section) (a) What is the relationship between the wavelength and the frequency of radiant energy? (b) Ozone in the upper atmosphere absorbs energy in the 210-230-nm range of the spectrum. In what region of the electromagnetic spectrum does this radiatio

Chapter: Problem: 13E

Chemistry: The Central Science 13
Problem 13E The Wave Nature of Light (Section) What are the basic SI units for (a) the wavelength of light, (b) the frequency of light, (c) the speed of light?

Chapter: Problem: 16E

Chemistry: The Central Science 13
Problem 16E The Wave Nature of Light (Section) Determine which of the following statements are false and correct them, (a) The frequency of radiation increases as the wavelength increases, (b) Electromagnetic radiation travels through a vacuum at a constant speed, regardless of wavelength, (c) Infr

Chapter: Problem: 15E

Chemistry: The Central Science 13
Problem 15E The Wave Nature of Light (Section) Label each of the following statements as true or false. For those that are false, correct the statement, (a) Visible light is a form of electromagnetic radiation, (b) Ultraviolet light has longer wavelengths than visible light, (c) X rays travel faste

Chapter: Problem: 17E

Chemistry: The Central Science 13
Problem 17E The Wave Nature of Light (Section) Arrange the following kinds of electromagnetic radiation in order of increasing wavelength infrared, green light, red light, radio waves. X rays, ultraviolet light.

Chapter: Problem: 18E

Chemistry: The Central Science 13
Problem 18E The Wave Nature of Light (Section) List the following types of electromagnetic radiation in order of increasing wavelength: (a) the gamma rays produced by a radioactive nuclide used in medical imaging; (b) radiation from an FM radio station at 93.1 MHz on the dial; (c) a radio signal fr

Chapter: Problem: 19E

Chemistry: The Central Science 13
Problem 19E The Wave Nature of Light (Section) (a) What is the frequency of radiation that has a wavelength of 10 pm. about the size of a bacterium? (b) What is the wavelength of radiation that has a frequency of 5.50 x 1014 s-1? (c) Would the radiations in part (a) or part (b) be visible to the hu

Chapter: Problem: 20E

Chemistry: The Central Science 13
Problem 20E The Wave Nature of Light (Section) (a) What is the frequency of radiation whose wavelength is 0.86 nm? (b) What is the wavelength of radiation that has a frequency of 6.4 x 1011 s-1? (c) Would the radiations in part (a) or part (b) be detected by an X-ray detector? (d) What distance doe

Chapter: Problem: 21E

Chemistry: The Central Science 13
The Wave Nature of Light (Section 6.1) A laser pointer used in a lecture hall emits light at \(650 \mathrm{~nm}\). What is the frequency of this radiation? Using Figure 6.4, predict the color associated with this wavelength. Equation Transcription: Text Tr

Chapter: Problem: 23E

Chemistry: The Central Science 13
Problem 23E Quantized Energy and Photons (Section) If human height were quantized in 1-foot increments, what would happen to the height of a child as she grows up: (i) The childs height would never change, (ii) the childs height would continuously get greater, (iii) the child's height would increas

Chapter: Problem: 22E

Chemistry: The Central Science 13
Problem 22E The Wave Nature of Light (Section) It is possible to convert radiant energy into electrical energy using photovoltaic cells. Assuming equal efficiency of conversion, would infrared or ultraviolet radiation yield more electrical energy on a per-photon basis?

Chapter: Problem: 24E

Chemistry: The Central Science 13
Problem 24E Quantized Energy and Photons (Section) Einsteins 1905 paper on the photoelectric effect was the first important application of Plancks quantum hypothesis. Describe Plancks original hypothesis, and explain how Einstein made use of it in his theory of the photoelectric effect.

Chapter: Problem: 25E

Chemistry: The Central Science 13
Problem 25E Quantized Energy and Photons (Section) (a) Calculate the energy of a photon of electromagnetic radiation whose frequency is 2.94 x 1014 s-1. (b) Calculate the energy of a photon of radiation whose wavelength is 413 nm. (c) What wavelength of radiation has photons of energy 6.06 x 10-19

Chapter: Problem: 26E

Chemistry: The Central Science 13
Problem 26E Quantized Energy and Photons (Section) (a) A green laser pointer emits light with a wavelength of 532 nm. What is the frequency of this light? (b) What is the energy of one of these photons? (c) The laser pointer emits light because electrons in the material are excited (by a battery) f

Chapter: Problem: 27E

Chemistry: The Central Science 13
The Wave Nature of Light (Section 6.1) (a) Calculate and compare the energy of a photon of wavelength \(3.3 \mu \mathrm{m}\) with that of wavelength \(0.154 \mathrm{~nm}\) (b) Use Figure 6.4 to identify the region of the electromagnetic spectrum to which each belongs.

Chapter: Problem: 28E

Chemistry: The Central Science 13
Problem 28E Quantized Energy and Photons (Section) An AM radio station broadcasts at 1010 KHz. and its FM partner broadcasts at 98.3 MHz. Calculate and compare the energy of the photons emitted by these two radio stations.

Chapter: Problem: 29E

Chemistry: The Central Science 13
Problem 29E Quantized Energy and Photons (Section) One type of sunburn occurs on exposure to UV light of wavelength in the vicinity of 325 nm. (a) What is the energy of a photon of this wavelength? (b) What is the energy of a mole of these photons? (c) How many photons are in a 1.00 mJ burst of t

Chapter: Problem: 30E

Chemistry: The Central Science 13
Problem 30E Quantized Energy and Photons (Section) The energy from radiation can be used to cause the rupture of chemical bonds. A minimum energy of 242 kJ/mol is required to break the chlorine-chlorine bond in CI2. What is the longest wavelength of radiation that possesses the necessary energy to

Chapter: Problem: 31E

Chemistry: The Central Science 13
Problem 31E Quantized Energy and Photons (Section) A diode laser emits at a wavelength of 987 nm. (a) In what portion of the electromagnetic spectrum is this radiation found? (b) All of its output energy is absorbed in a detector that measures a total energy of 0.52 J over a period of 32 s. How man

Chapter: Problem: 32E

Chemistry: The Central Science 13
Problem 32E Quantized Energy and Photons (Section) A stellar object is emitting radiation at 3.55 mm. (a) What type of electromagnetic spectrum is this radiation? (b) If a detector is capturing 3.2 x 108 photons per second at this wavelength, what is the total energy of the photons detected in 1.0

Chapter: Problem: 33E

Chemistry: The Central Science 13
Problem 33E Quantized Energy and Photons (Section) Molybdenum metal must absorb radiation with a minimum frequency of 1.09 x 1015 s-1 before it can eject an electron from its surface via the photoelectric effect, (a) What is the minimum energy needed to eject an electron? (b) What wavelength of rad

Chapter: Problem: 34E

Chemistry: The Central Science 13
Problem 34E Quantized Energy and Photons (Section) Titanium metal requires a photon with a minimum energy of 6.94 x 10-19 J to emit electrons, (a) What is the minimum frequency of light necessary to emit electrons from titanium via the photoelectric effect? (b) What is the wavelength of this light?

Chapter: Problem: 35E

Chemistry: The Central Science 13
Problem 35E Bohrs Model; Matter Waves (Sections) Explain how the existence of line spectra is consistent with Bohr's theory of quantized energies for the electron in the hydrogen atom.

Chapter: Problem: 36E

Chemistry: The Central Science 13
Problem 36E Bohrs Model; Matter Waves (Sections) (a) Consider the following three statements: (i) A hydrogen atom in the n = 3 state can emit light at only two specific wavelengths, (ii) a hydrogen atom in the n = 2 state is at a lower energy than the n = 1 state, and (iii) the energy of an em

Chapter: Problem: 37E

Chemistry: The Central Science 13
Problem 37E Bohrs Model; Matter Waves (Sections) Is energy emitted or absorbed when the following electronic transitions occur in hydrogen? (a) from n = 4 to n = 2, (b) from an orbit of radius 2.12 A to one of radius 8.46 A. (c) an electron adds to the H+ ion and ends up in the n = 3 shell?

Chapter: Problem: 38E

Chemistry: The Central Science 13
Problem 38E Bohrs Model; Matter Waves (Sections) Indicate whether energy is emitted or absorbed when the following electronic transitions occur in hydrogen: (a) from n = 2 to n = 6, (b) from an orbit of radius 4.76 A to one of radius 0.529 A. (c) from the n = 6 to the n = 9 state.

Chapter: Problem: 39E

Chemistry: The Central Science 13
Bohrs Model; Matter Waves (Sections 6.3 and 6.4) (a) Using Equation 6.5, calculate the energy of an electron in the hydrogen atom when \(n=2\) and when \(n=6\). Calculate the wavelength of the radiation released when an electron moves from \(n=6 \text { to } n=2\) (b) Is this line in the vi

Chapter: Problem: 40E

Chemistry: The Central Science 13
Problem 40E Bohrs Model; Matter Waves (Sections) Consider a transition of the electron in the hydrogen atom from n = 4 to n = 9. (a) Is AE for this process positive or negative? (b) Determine the wavelength of light that is associated with this transition. Will the light be absorbed or emitted? (c)

Chapter: Problem: 41E

Chemistry: The Central Science 13
The visible emission lines observed by Balmer all involved \(n_{f}=2\). (a) Which of the following is the best explanation of why the lines with \(n_{f}=3\) are not observed in the visible portion of the spectrum: (i) Transitions to \(n_{f}=3\) are not allowed to happen, (ii) transition

Chapter: Problem: 42E

Chemistry: The Central Science 13
Problem 42E Bohrs Model; Matter Waves (Sections) The Lyman series of emission lines of the hydrogen atom are those for which nf = 1. (a) Determine the region of the electromagnetic spectrum in which the lines of the Lyman series are observed, (b) Calculate the wavelengths of the first three li

Chapter: Problem: 45E

Chemistry: The Central Science 13
Problem 45E Bohrs Model; Matter Waves (Sections) Order the following transitions in the hydrogen atom from smallest to largest frequency of light absorbed: n = 3ton = 6, n = 4ton = 9. n = 2ton = 3, and n = 1 to n = 2.

Chapter: Problem: 43E

Chemistry: The Central Science 13
Problem 43E Bohrs Model; Matter Waves (Sections) One of the emission lines of the hydrogen atom has a wavelength of 93.07 nm. (a) In what region of the electromagnetic spectrum is this emission found? (b) Determine the initial and final values of n associated with this emission.

Chapter: Problem: 46E

Chemistry: The Central Science 13
Problem 46E Bohrs Model; Matter Waves (Sections) Place the following transitions of the hydrogen atom in order from shortest to longest wavelength of the photon emitted: n = 5 to n = 3, n = 4 to n = 2, n = 7 to n = 4. and n = 3 to n =2.

Chapter: Problem: 44E

Chemistry: The Central Science 13
Problem 44E Bohrs Model; Matter Waves (Sections) The hydrogen atom can absorb light of wavelength 1094 nm. (a) In what region of the electromagnetic spectrum is this absorption found? (b) Determine the initial and final values of n associated with this absorption.

Chapter: Problem: 48E

Chemistry: The Central Science 13
Problem 48E Bohrs Model; Matter Waves (Sections) Among the elementary subatomic particles of physics is the muon, which decays within a few nanoseconds after formation. The muon has a rest mass 206.8 times that of an electron. Calculate the de Broglie wavelength associated with a muon traveling at

Chapter: Problem: 47E

Chemistry: The Central Science 13
Problem 47E Bohrs Model; Matter Waves (Sections) Use the de Broglie relationship to determine the wavelengths of the following objects: (a) an 85-kg person skiing at 50 km/hr, (b) a 10.0-g bullet fired at 250 m/s, (c) a lithium atom moving at 2.5 x 105 m/s, (d) an ozone (03) molecule in the upper a

Chapter: Problem: 49E

Chemistry: The Central Science 13
Problem 49E Bohrs Model; Matter Waves (Sections) Neutron diffraction is an important technique for determining the structures of molecules. Calculate the velocity of a neutron needed to achieve a wavelength of 1.25 A. (Refer to the inside cover for the mass of the neutron.)

Chapter: Problem: 50E

Chemistry: The Central Science 13
Problem 50E Bohrs Model; Matter Waves (Sections) The electron microscope has been widely used to obtain highly magnified images of biological and other types of materials. When an electron is accelerated through a particular potential field, it attains a speed of 9.47 x 106 m/s. What is the charact

Chapter: Problem: 51E

Chemistry: The Central Science 13
Problem 51E Bohrs Model; Matter Waves (Sections) Using Heisenberg's uncertainty principle, calculate the uncertainty in the position of (a) a 1.50-mg mosquito moving at a speed of 1.40 m/s if the speed is Known to within 0.01 m/s; (b) a proton moving at a speed of (5.00 0.01) x 104 m/s. (The mass

Chapter: Problem: 52E

Chemistry: The Central Science 13
Problem 52E Bohrs Model; Matter Waves (Sections) Calculate the uncertainty in the position of (a) an electron moving at a speed of (3.00 0.01) x 105 m/s, (b) a neutron moving at this same speed (The masses of an electron and a neutron are given in the table of fundamental constants in the inside c

Chapter: Problem: 53E

Chemistry: The Central Science 13
Problem 53E Quantum Mechanics and Atomic Orbitals (Sections) (a) Why does the Bohr model of the hydrogen atom violate the uncertainty principle? (b) In what way is the description of the electron using a wave function consistent with de Broglie's hypothesis? (c) What is meant by the term probabilit

Chapter: Problem: 55E

Chemistry: The Central Science 13
Problem 55E Quantum Mechanics and Atomic Orbitals (Sections) (a) For n = 4, what are the possible values of /? (b) For / = 2, what are the possible values of ml? (c) If ml is 2, what are the possible values for /?

Chapter: Problem: 54E

Chemistry: The Central Science 13
Problem 54E Quantum Mechanics and Atomic Orbitals (Sections) (a) According to the Bohr model, an electron in the ground state of a hydrogen atom orbits the nucleus at a specific radius of 0.53 A. In the quantum mechanical description of the hydrogen atom, the most probable distance of the electron

Chapter: Problem: 56E

Chemistry: The Central Science 13
Problem 56E Quantum Mechanics and Atomic Orbitals (Sections) How many possible values for / and ml are there when (a) n = 3, (b) n = 5?

Chapter: Problem: 57E

Chemistry: The Central Science 13
Problem 57E Quantum Mechanics and Atomic Orbitals (Sections) Give the numerical values of n and / corresponding to each of the following orbital designations: (a) 3p, (b) 2s,(c) 4f,(d) 5cf.

Chapter: Problem: 58E

Chemistry: The Central Science 13
Problem 58E Quantum Mechanics and Atomic Orbitals (Sections) Give the values for n, I, and ml for (a) each orbital in the 2p subshell, (b) each orbital in the 5d subshell.

Chapter: Problem: 60E

Chemistry: The Central Science 13
Problem 60E Quantum Mechanics and Atomic Orbitals (Sections) A hydrogen atom orbital has n = 5 and ml = -2. (a) What are the possible values of / for this orbital? (b) What are the possible values of ms for the orbital?

Chapter: Problem: 63E

Chemistry: The Central Science 13
Problem 63E Quantum Mechanics and Atomic Orbitals (Sections) Sketch the shape and orientation of the following types of orbitals: (a) s, (b) pz. (c) dxy.

Chapter: Problem: 62E

Chemistry: The Central Science 13
For the table that follows, write which orbital goes with the quantum numbers. Dont worry about \(x, y, z\) subscripts. If the quantum numbers are not allowed, write not allowed. Equation Transcription: Text Transcription: x,y,z

Chapter: Problem: 61E

Chemistry: The Central Science 13
Problem 61E Quantum Mechanics and Atomic Orbitals (Sections) Which of the following represent impossible combinations of n and /? (a) 1 p, (b) 4s, (c) 5f, (d) 2d

Chapter: Problem: 64E

Chemistry: The Central Science 13
Problem 64E Quantum Mechanics and Atomic Orbitals (Sections) Sketch the shape and orientation of the following types of orbitals: (a) px, (b) cfz2. (c) dx2 - y2.

Chapter: Problem: 65E

Chemistry: The Central Science 13
Problem 65E Quantum Mechanics and Atomic Orbitals (Sections) (a) What are the similarities of and differences between the 1s and 2s orbitals of the hydrogen atom? (b) In what sense does a 2p orbital have directional character? Compare the directional" characteristics of the px and cfx2- y2 orbital

Chapter: Problem: 66E

Chemistry: The Central Science 13
(a) With reference to Figure 6.19, what is the relationship between the number of nodes in an s orbital and the value of the principal quantum number? (b) Identify the number of nodes; that is, identify places where the electron density is zero, in the \(2 p_{x}\) orbital; in the \(3 s\) orbital

Chapter: Problem: 68E

Chemistry: The Central Science 13
Problem 68E Many-Electron Atoms and Electron Configurations (Sections) (a) The average distance from the nucleus of a 3s electron in a chlorine atom is smaller than that for a 3p electron. In light of this fact, which orbital is higher in energy? (b) Would you expect it to require more or less ener

Chapter: Problem: 67E

Chemistry: The Central Science 13
Problem 67E Many-Electron Atoms and Electron Configurations (Sections) For a given value of the principal quantum number, n, how do the energies of the s, p, d. and f subshells vary for (a) hydrogen, (b) a many-electron atom?

Chapter: Problem: 70E

Chemistry: The Central Science 13
Problem 70E Many-Electron Atoms and Electron Configurations (Sections) (a) State the Pauli exclusion principle in your own words, (b) The Pauli exclusion principle is, in an important sense, the Key to understanding the periodic table, (c) Explain.

Chapter: Problem: 69E

Chemistry: The Central Science 13
Problem 69E Many-Electron Atoms and Electron Configurations (Sections) (a) What experimental evidence is there for the electron having a spin"? (b) Draw an energy-level diagram that shows the relative energetic positions of a 1s orbital and a 2s orbital. Put two electrons in the 1s orbital, (c) Dra

Chapter: Problem: 71E

Chemistry: The Central Science 13
Problem 71E Many-Electron Atoms and Electron Configurations (Sections) What is the maximum number of electrons that can occupy each of the following subshells? (a) 3P, (b) 5a, (c) 2s, (d) 4f.

Chapter: Problem: 73E

Chemistry: The Central Science 13
Problem 73E Many-Electron Atoms and Electron Configurations (Sections) (a) What are valence electrons"? (b) What are core electrons"? (c) What does each box in an orbital diagram represent? (d) What quantity is represented by the half arrows in an orbital diagram?

Chapter: Problem: 72E

Chemistry: The Central Science 13
Problem 72E Many-Electron Atoms and Electron Configurations (Sections) What is the maximum number of electrons in an atom that can have the following quantum numbers? (a) n = 3, m\ = -2; (b) n = 4, / = 3; (c) n = 5, / = 3, ml = 2, (d) n = 4, / = 1, ml = 0.

Chapter: Problem: 74E

Chemistry: The Central Science 13
Problem 74E Many-Electron Atoms and Electron Configurations (Sections) For each element, indicate the number of valence electrons, core electrons, and unpaired electrons in the ground state: (a) nitrogen, (b) silicon, (c) chlorine.

Chapter: Problem: 76E

Chemistry: The Central Science 13
Problem 76E Many-Electron Atoms and Electron Configurations (Sections) Write the condensed electron configurations for the following atoms and indicate how many unpaired electrons each has: (a) Mg, (b) Ge. (c) Br, (d) V, (e) Y, (f) Lu.

Chapter: Problem: 75E

Chemistry: The Central Science 13
Problem 75E Many-Electron Atoms and Electron Configurations (Sections) Write the condensed electron configurations for the following atoms, using the appropriate noble-gas core abbreviations: (a) Cs, (b) Ni, (c) Se. (d) Cd. (e) U, (f) Pb.

Chapter: Problem: 77E

Chemistry: The Central Science 13
Problem 77E Many-Electron Atoms and Electron Configurations (Sections) Identify the specific element that corresponds to each of the following electron configurations and indicate the number of unpaired electrons for each: (a) 1s22s2. (b) 1s22s22p4. (c) [Ar]4s13d5, (d) [Kr]5s24cf105p4.

Chapter: Problem: 78E

Chemistry: The Central Science 13
Problem 78E Many-Electron Atoms and Electron Configurations (Sections) Identify the group of elements that corresponds to each of the following generalized electron configurations and indicate the number of unpaired electrons for each: (a) [noble gas] ns2np5 (b) [noble gas] ns2(n - 1)d2

Chapter: Problem: 6.1

Chemistry: The Central Science 13
Consider the water wave shown here. (a) How could you measure the speed of this wave? (b) How would you determine the wavelength of the wave? (c) Given the speed and wavelength of the wave, how could you determine the frequency of the wave? (d) Suggest an independent experiment to determine the frequ

Chapter: Problem: 6.2

Chemistry: The Central Science 13
A popular kitchen appliance produces electromagnetic radiation with a frequency of 2450 MHz. With reference to Figure 6.4, answer the following: (a) Estimate the wavelength of this radiation. (b) Would the radiation produced by the appliance be visible to the human eye? (c) If the radiation is not vi

Chapter: Problem: 6.3

Chemistry: The Central Science 13
The following diagrams represent two electromagnetic waves. Which wave corresponds to the higher- energy radiation? [Section 6.2] (a) (b)

Chapter: Problem: 6.4

Chemistry: The Central Science 13
As shown in the accompanying photograph, an electric stove burner on its highest setting exhibits an orange glow. (a) When the burner setting is changed to low, the burner continues to produce heat but the orange glow disappears. How can this observation be explained with reference to one of the fund

Chapter: Problem: 6.5

Chemistry: The Central Science 13
Stars do not all have the same temperature. The color of light emitted by stars is characteristic of the light emitted by hot objects. Telescopic photos of three stars are shown below: (i) the Sun, which is classified as a yellow star, (ii) Rigel, in the constellation Orion, which is classified as a

Chapter: Problem: 6.6

Chemistry: The Central Science 13
The familiar phenomenon of a rainbow results from the diffraction of sunlight through raindrops. (a) Does the wavelength of light increase or decrease as we proceed outward from the innermost band of the rainbow? (b) Does the frequency of light increase or decrease as we proceed outward? (c) Suppose

Chapter: Problem: 6.7

Chemistry: The Central Science 13
A certain quantum mechanical system has the energy levels shown in the accompanying diagram. The energy levels are indexed by a single quantum number n that is an integer. (a) As drawn, which quantum numbers are involved in the transition that requires the most energy? (b) Which quantum numbers are i

Chapter: Problem: 6.8

Chemistry: The Central Science 13
Consider a fictitious one-dimensional system with one electron. The wave function for the electron, drawn below, is c1x2 = sin x from x = 0 to x = 2p. (a) Sketch the probability density, c2 1x2, from x = 0 to x = 2p. (b) At what value or values of x will there be the greatest probability of finding t

Chapter: Problem: 6.9

Chemistry: The Central Science 13
The contour representation of one of the orbitals for the n = 3 shell of a hydrogen atom is shown as follows. (a) What is the quantum number l for this orbital? (b) How do we label this orbital? (c) In which of the following ways would you modify this sketch to show the analogous orbital for the n =

Chapter: Problem: 6.10

Chemistry: The Central Science 13
The accompanying drawing shows the shape of a d orbital. (a) Based on the shape, how many of the d orbitals could it be? (b) Which of the following would you need to determine which of the d orbitals it is: (i) the direction of the z-axis, (ii) the identity of the element, (iii) the number of electro

Chapter: Problem: 6.11

Chemistry: The Central Science 13
The accompanying drawing shows part of the orbital diagram for an element. (a) As drawn, the drawing is incorrect. Why? (b) How would you correct the drawing without changing the number of electrons? (c) To which group in the periodic table does the element belong? [Section 6.8]

Chapter: Problem: 6.12

Chemistry: The Central Science 13
State where in the periodic table these elements appear: (a) elements with the valence-shell electron configuration ns 2 np5 (b) elements that have three unpaired p electrons (c) an element whose valence electrons are 4s 2 4p1 (d) the d-block elements [Section 6.9]

Chapter: Problem: 6.13

Chemistry: The Central Science 13
What are the basic SI units for (a) the wavelength of light, (b) the frequency of light, (c) the speed of light?

Chapter: Problem: 6.14a

Chemistry: The Central Science 13
(a) What is the relationship between the wavelength and the frequency of radiant energy?

Chapter: Problem: 6.14b

Chemistry: The Central Science 13
(b) Ozone in the upper atmosphere absorbs energy in the 210230-nm range of the spectrum. In what region of the electromagnetic spectrum does this radiation occur?

Chapter: Problem: 6.15

Chemistry: The Central Science 13
Label each of the following statements as true or false. For those that are false, correct the statement. (a) Visible light is a form of electromagnetic radiation. (b) Ultraviolet light has longer wavelengths than visible light. (c) X rays travel faster than microwaves. (d) Electromagnetic radiation

Chapter: Problem: 6.16

Chemistry: The Central Science 13
Determine which of the following statements are false and correct them. (a) The frequency of radiation increases as the wavelength increases. (b) Electromagnetic radiation travels through a vacuum at a constant speed, regardless of wavelength. (c) Infrared light has higher frequencies than visible li

Chapter: Problem: 6.17

Chemistry: The Central Science 13
Arrange the following kinds of electromagnetic radiation in order of increasing wavelength: infrared, green light, red light, radio waves, X rays, ultraviolet light.

Chapter: Problem: 6.18

Chemistry: The Central Science 13
List the following types of electromagnetic radiation in order of increasing wavelength: (a) the gamma rays produced by a radioactive nuclide used in medical imaging; (b) radiation from an FM radio station at 93.1 MHz on the dial; (c) a radio signal from an AM radio station at 680 kHz on the dial; (d

Chapter: Problem: 6.19a

Chemistry: The Central Science 13
(a) What is the frequency of radiation that has a wavelength of 10 mm, about the size of a bacterium?

Chapter: Problem: 6.19b

Chemistry: The Central Science 13
(b) What is the wavelength of radiation that has a frequency of 5.50 * 1014 s- 1 ?

Chapter: Problem: 6.19c

Chemistry: The Central Science 13
(c) Would the radiations in part (a) or part (b) be visible to the human eye?

Chapter: Problem: 6.19d

Chemistry: The Central Science 13
(d) What distance does electromagnetic radiation travel in 50.0 ms?

Chapter: Problem: 6.20a

Chemistry: The Central Science 13
(a) What is the frequency of radiation whose wavelength is 0.86 nm?

Chapter: Problem: 6.20b

Chemistry: The Central Science 13
(b) What is the wavelength of radiation that has a frequency of 6.4 * 1011 s- 1 ?

Chapter: Problem: 6.20c

Chemistry: The Central Science 13
(c) Would the radiations in part (a) or part (b) be detected by an X-ray detector?

Chapter: Problem: 6.20d

Chemistry: The Central Science 13
What distance does electromagnetic radiation travel in 0.38 ps?

Chapter: Problem: 6.21

Chemistry: The Central Science 13
A laser pointer used in a lecture hall emits light at 650 nm. What is the frequency of this radiation? Using Figure 6.4, predict the color associated with this wavelength.

Chapter: Problem: 6.22

Chemistry: The Central Science 13
It is possible to convert radiant energy into electrical energy using photovoltaic cells. Assuming equal efficiency of conversion, would infrared or ultraviolet radiation yield more electrical energy on a per- photon basis?

Chapter: Problem: 6.23

Chemistry: The Central Science 13
If human height were quantized in 1-foot increments, what would happen to the height of a child as she grows up: (i) The childs height would never change, (ii) the childs height would continuously get greater, (iii) the childs height would increase in jumps of 1 foot at a time, or (iv) the childs hei

Chapter: Problem: 6.24

Chemistry: The Central Science 13
Einsteins 1905 paper on the photoelectric effect was the first important application of Plancks quantum hypothesis. Describe Plancks original hypothesis, and explain how Einstein made use of it in his theory of the photoelectric effect.

Chapter: Problem: 6.25a

Chemistry: The Central Science 13
(a) Calculate the energy of a photon of electromagnetic radiation whose frequency is 2.94 * 1014 s- 1 .

Chapter: Problem: 6.25b

Chemistry: The Central Science 13
(b) Calculate the energy of a photon of radiation whose wavelength is 413 nm.

Chapter: Problem: 6.25c

Chemistry: The Central Science 13
(c) What wavelength of radiation has photons of energy 6.06 * 10 - 19 J?

Chapter: Problem: 6.26a

Chemistry: The Central Science 13
(a) A green laser pointer emits light with a wavelength of 532 nm. What is the frequency of this light?

Chapter: Problem: 6.26b

Chemistry: The Central Science 13
(b) What is the energy of one of these photons.

Chapter: Problem: 6.26c

Chemistry: The Central Science 13
(c) The laser pointer emits light because electrons in the material are excited (by a battery) from their ground state to an upper excited state. When the electrons return to the ground state, they lose the excess energy in the form of 532-nm photons. What is the energy gap between the ground state a

Chapter: Problem: 6.27a

Chemistry: The Central Science 13
a) Calculate and compare the energy of a photon of wavelength 3.3 mm with that of wavelength 0.154 nm.

Chapter: Problem: 6.27b

Chemistry: The Central Science 13
(b) Use Figure 6.4 to identify the region of the electromagnetic spectrum to which each belongs.

Chapter: Problem: 6.28

Chemistry: The Central Science 13
An AM radio station broadcasts at 1010 kHz, and its FM partner broadcasts at 98.3 MHz. Calculate and compare the energy of the photons emitted by these two radio stations.

Chapter: Problem: 6.29

Chemistry: The Central Science 13
One type of sunburn occurs on exposure to UV light of wavelength in the vicinity of 325 nm. (a) What is the energy of a photon of this wavelength? (b) What is the energy of a mole of these photons? (c) How many photons are in a 1.00 mJ burst of this radiation? (d) These UV photons can break chemical

Chapter: Problem: 6.30

Chemistry: The Central Science 13
The energy from radiation can be used to cause the rupture of chemical bonds. A minimum energy of 242 kJ>mol is required to break the chlorinechlorine bond in Cl2. What is the longest wavelength of radiation that possesses the necessary energy to break the bond? What type of electromagnetic radiation

Chapter: Problem: 6.31

Chemistry: The Central Science 13
A diode laser emits at a wavelength of 987 nm. (a) In what portion of the electromagnetic spectrum is this radiation found? (b) All of its output energy is absorbed in a detector that measures a total energy of 0.52 J over a period of 32 s. How many photons per second are being emitted by the laser?

Chapter: Problem: 6.32

Chemistry: The Central Science 13
A stellar object is emitting radiation at 3.55 mm. (a) What type of electromagnetic spectrum is this radiation? (b) If a detector is capturing 3.2 * 108 photons per second at this wavelength, what is the total energy of the photons detected in 1.0 hour?

Chapter: Problem: 6.33

Chemistry: The Central Science 13
Molybdenum metal must absorb radiation with a minimum frequency of 1.09 * 1015 s- 1 before it can eject an electron from its surface via the photoelectric effect. (a) What is the minimum energy needed to eject an electron? (b) What wavelength of radiation will provide a photon of this energy? (c) If

Chapter: Problem: 6.34

Chemistry: The Central Science 13
Titanium metal requires a photon with a minimum energy of 6.94 * 10 - 19 J to emit electrons. (a) What is the minimum frequency of light necessary to emit electrons from titanium via the photoelectric effect? (b) What is the wavelength of this light? (c) Is it possible to eject electrons from titaniu

Chapter: Problem: 6.35

Chemistry: The Central Science 13
Explain how the existence of line spectra is consistent with Bohrs theory of quantized energies for the electron in the hydrogen atom.

Chapter: Problem: 6.36a

Chemistry: The Central Science 13
(a) Consider the following three statements: (i) A hydrogen atom in the n = 3 state can emit light at only two specific wavelengths, (ii) a hydrogen atom in the n = 2 state is at a lower energy than the n = 1 state, and (iii) the energy of an emitted photon equals the energy difference of the two sta

Chapter: Problem: 6.36b

Chemistry: The Central Science 13
(b) Does a hydrogen atom expand or contract as it moves from its ground state to an excited state?

Chapter: Problem: 6.37

Chemistry: The Central Science 13
Is energy emitted or absorbed when the following electronic transitions occur in hydrogen? (a) from n = 4 to n = 2, (b) from an orbit of radius 2.12 to one of radius 8.46 , (c) an electron adds to the H+ ion and ends up in the n = 3 shell?

Chapter: Problem: 6.38

Chemistry: The Central Science 13
Indicate whether energy is emitted or absorbed when the following electronic transitions occur in hydrogen: (a) from n = 2 to n = 6, (b) from an orbit of radius 4.76 to one of radius 0.529 , (c) from the n = 6 to the n = 9 state

Chapter: Problem: 6.39a

Chemistry: The Central Science 13
(a) Using Equation 6.5, calculate the energy of an electron in the hydrogen atom when n = 2 and when n = 6. Calculate the wavelength of the radiation released when an electron moves from n = 6 to n = 2.

Chapter: Problem: 6.39b

Chemistry: The Central Science 13
(b) Is this line in the visible region of the electromagnetic spectrum? If so, what color is it?

Chapter: Problem: 6.40

Chemistry: The Central Science 13
Consider a transition of the electron in the hydrogen atom from n = 4 to n = 9. (a) Is E for this process positive or negative? (b) Determine the wavelength of light that is associated with this transition. Will the light be absorbed or emitted? (c) In which portion of the electromagnetic spectrum is

Chapter: Problem: 6.41

Chemistry: The Central Science 13
The visible emission lines observed by Balmer all involved nf = 2. (a) Which of the following is the best explanation of why the lines with nf = 3 are not observed in the visible portion of the spectrum: (i) Transitions to nf = 3 are not allowed to happen, (ii) transitions to nf = 3 emit photons in t

Chapter: Problem: 6.42

Chemistry: The Central Science 13
The Lyman series of emission lines of the hydrogen atom are those for which nf = 1. (a) Determine the region of the electromagnetic spectrum in which the lines of the Lyman series are observed. (b) Calculate the wavelengths of the first three

Chapter: Problem: 6.43

Chemistry: The Central Science 13
One of the emission lines of the hydrogen atom has a wavelength of 93.07 nm. (a) In what region of the electromagnetic spectrum is this emission found? (b) Determine the initial and final values of n associated with this emission

Chapter: Problem: 6.44

Chemistry: The Central Science 13
The hydrogen atom can absorb light of wavelength 1094 nm. (a) In what region of the electromagnetic spectrum is this absorption found? (b) Determine the initial and final values of n associated with this absorption.

Chapter: Problem: 6.45

Chemistry: The Central Science 13
Order the following transitions in the hydrogen atom from smallest to largest frequency of light absorbed: n = 3 to n = 6, n = 4 to n = 9, n = 2 to n = 3, and n = 1 to n = 2

Chapter: Problem: 6.46

Chemistry: The Central Science 13
Place the following transitions of the hydrogen atom in order from shortest to longest wavelength of the photon emitted: n = 5 to n = 3, n = 4 to n = 2, n = 7 to n = 4, and n = 3 to n = 2

Chapter: Problem: 6.47

Chemistry: The Central Science 13
Use the de Broglie relationship to determine the wavelengths of the following objects: (a) an 85-kg person skiing at 50 km>hr, (b) a 10.0-g bullet fired at 250 m>s, (c) a lithium atom moving at 2.5 * 105 m>s, (d) an ozone 1O32 molecule in the upper atmosphere moving at 550 m>s.

Chapter: Problem: 6.48

Chemistry: The Central Science 13
Among the elementary subatomic particles of physics is the muon, which decays within a few nanoseconds after formation. The muon has a rest mass 206.8 times that of an electron. Calculate the de Broglie wavelength associated with a muon traveling at 8.85 * 105 cm>s.

Chapter: Problem: 6.49

Chemistry: The Central Science 13
Neutron diffraction is an important technique for determining the structures of molecules. Calculate the velocity of a neutron needed to achieve a wavelength of 1.25 . (Refer to the inside cover for the mass of the neutron.)

Chapter: Problem: 6.50

Chemistry: The Central Science 13
The electron microscope has been widely used to obtain highly magnified images of biological and other types of materials. When an electron is accelerated through a particular potential field, it attains a speed of 9.47 * 106 m>s. What is the characteristic wavelength of this electron? Is the wavelen

Chapter: Problem: 6.51

Chemistry: The Central Science 13
Using Heisenbergs uncertainty principle, calculate the uncertainty in the position of (a) a 1.50-mg mosquito moving at a speed of 1.40 m>s if the speed is known to within {0.01 m>s; (b) a proton moving at a speed of 15.00 { 0.012 * 104 m>s. (The mass of a proton is given in the table of fundamental c

Chapter: Problem: 6.52

Chemistry: The Central Science 13
Calculate the uncertainty in the position of (a) an electron moving at a speed of 13.00 { 0.012 * 105 m>s, (b) a neutron moving at this same speed. (The masses of an electron and a neutron are given in the table of fundamental constants in the inside cover of the text.) (c) Based on your answers to p

Chapter: Problem: 6.53a

Chemistry: The Central Science 13
(a) Why does the Bohr model of the hydrogen atom violate the uncertainty principle?

Chapter: Problem: 6.53b

Chemistry: The Central Science 13
(b) In what way is the description of the electron using a wave function consistent with de Broglies hypothesis?

Chapter: Problem: 6.53c

Chemistry: The Central Science 13
(c) What is meant by the term probability density? Given the wave function, how do we find the probability density at a certain point in space?

Chapter: Problem: 6.54a

Chemistry: The Central Science 13
(a) According to the Bohr model, an electron in the ground state of a hydrogen atom orbits the nucleus at a specific radius of 0.53 . In the quantum mechanical description of the hydrogen atom, the most probable distance of the electron from the nucleus is 0.53 . Why are these two statements differen

Chapter: Problem: 6.54b

Chemistry: The Central Science 13
(b) Why is the use of Schrdingers wave equation to describe the location of a particle very different from the description obtained from classical physics? (c) In the quantum mechanical description of an electron, what is the physical significance of the square of the wave function, c2 ?

Chapter: Problem: 6.55a

Chemistry: The Central Science 13
(a) For n = 4, what are the possible values of l?

Chapter: Problem: 6.55b

Chemistry: The Central Science 13
(b) For l = 2, what are the possible values of ml ? (c) If ml is 2, what are the possible values for l?

Chapter: Problem: 6.56

Chemistry: The Central Science 13
How many possible values for l and ml are there when (a) n = 3, (b) n = 5?

Chapter: Problem: 6.57

Chemistry: The Central Science 13
Give the numerical values of n and l corresponding to each of the following orbital designations: (a) 3p, (b) 2s, (c) 4f, (d) 5d

Chapter: Problem: 6.58

Chemistry: The Central Science 13
Give the values for n, l, and ml for (a) each orbital in the 2p subshell, (b) each orbital in the 5d subshell.

Chapter: Problem: 6.59

Chemistry: The Central Science 13
A certain orbital of the hydrogen atom has n = 4 and l = 2. (a) What are the possible values of ml for this orbital? (b) What are the possible values of ms for the orbital?

Chapter: Problem: 6.60

Chemistry: The Central Science 13
A hydrogen atom orbital has n = 5 and ml = -2. (a) What are the possible values of l for this orbital? (b) What are the possible values of ms for the orbital?

Chapter: Problem: 6.61

Chemistry: The Central Science 13
Which of the following represent impossible combinations of n and l? (a) 1p, (b) 4s, (c) 5f, (d) 2d

Chapter: Problem: 6.62

Chemistry: The Central Science 13
For the table that follows, write which orbital goes with the quantum numbers. Dont worry about x, y, z subscripts. If the quantum numbers are not allowed, write not allowed. N l ml Orbital 2 1 -1 2p (example) 1 0 0 3 -3 2 3 2 -2 2 0 -1 0 0 0 4 2 1 5 3 0

Chapter: Problem: 6.63

Chemistry: The Central Science 13
Sketch the shape and orientation of the following types of orbitals: (a) s, (b) pz, (c) dxy.

Chapter: Problem: 6.64

Chemistry: The Central Science 13
Sketch the shape and orientation of the following types of orbitals: (a) px, (b) dz2, (c) dx2 - y2.

Chapter: Problem: 6.65a

Chemistry: The Central Science 13
(a) What are the similarities of and differences between the 1s and 2s orbitals of the hydrogen atom?

Chapter: Problem: 6.65b

Chemistry: The Central Science 13
(b) In what sense does a 2p orbital have directional character? Compare the directional characteristics of the px and dx2 - y2 orbitals. (That is, in what direction or region of space is the electron density concentrated?)

Chapter: Problem: 6.65c

Chemistry: The Central Science 13
(c) What can you say about the average distance from the nucleus of an electron in a 2s orbital as compared with a 3s orbital?

Chapter: Problem: 6.65d

Chemistry: The Central Science 13
(d) For the hydrogen atom, list the following orbitals in order of increasing energy (that is, most stable ones first): 4f, 6s, 3d, 1s, 2p

Chapter: Problem: 6.66a

Chemistry: The Central Science 13
(a) With reference to Figure 6.19, what is the relationship between the number of nodes in an s orbital and the value of the principal quantum number?

Chapter: Problem: 6.66b

Chemistry: The Central Science 13
(b) Identify the number of nodes; that is, identify places where the electron density is zero, in the 2px orbital; in the 3s orbital.

Chapter: Problem: 6.66c

Chemistry: The Central Science 13
(c) What information is obtained from the radial probability functions in Figure 6.19?

Chapter: Problem: 6.66d

Chemistry: The Central Science 13
(d) For the hydrogen atom, list the following orbitals in order of increasing energy: 3s, 2s, 2p, 5s, 4d.

Chapter: Problem: 6.67

Chemistry: The Central Science 13
For a given value of the principal quantum number, n, how do the energies of the s, p, d, and f subshells vary for (a) hydrogen, (b) a many-electron atom?

Chapter: Problem: 6.68a

Chemistry: The Central Science 13
(a) The average distance from the nucleus of a 3s electron in a chlorine atom is smaller than that for a 3p electron. In light of this fact, which orbital is higher in energy?

Chapter: Problem: 6.68b

Chemistry: The Central Science 13
(b) Would you expect it to require more or less energy to remove a 3s electron from the chlorine atom, as compared with a 2p electron?

Chapter: Problem: 6.69a

Chemistry: The Central Science 13
(a) What experimental evidence is there for the electron having a spin?

Chapter: Problem: 6.69b

Chemistry: The Central Science 13
(b) Draw an energy-level diagram that shows the relative energetic positions of a 1s orbital and a 2s orbital. Put two electrons in the 1s orbital.

Chapter: Problem: 6.69c

Chemistry: The Central Science 13
(c) Draw an arrow showing the excitation of an electron from the 1s to the 2s orbital.

Chapter: Problem: 6.70a

Chemistry: The Central Science 13
(a) State the Pauli exclusion principle in your own words.

Chapter: Problem: 6.70b

Chemistry: The Central Science 13
(b) The Pauli exclusion principle is, in an important sense, the key to understanding the periodic table.

Chapter: Problem: 6.70c

Chemistry: The Central Science 13
(c) Explain

Chapter: Problem: 6.71

Chemistry: The Central Science 13
What is the maximum number of electrons that can occupy each of the following subshells? (a) 3p, (b) 5d, (c) 2s, (d) 4f

Chapter: Problem: 6.72

Chemistry: The Central Science 13
What is the maximum number of electrons in an atom that can have the following quantum numbers? (a) n = 3, ml = -2; (b) n = 4, l = 3;(c) n = 5, l = 3, ml = 2, (d) n = 4, l = 1, ml = 0.

Chapter: Problem: 6.73a

Chemistry: The Central Science 13
(a) What are valence electrons?

Chapter: Problem: 6.73b

Chemistry: The Central Science 13
(b) What are core electrons?

Chapter: Problem: 6.73c

Chemistry: The Central Science 13
(c) What does each box in an orbital diagram represent?

Chapter: Problem: 6.73d

Chemistry: The Central Science 13
(d) What quantity is represented by the half arrows in an orbital diagram?

Chapter: Problem: 6.74

Chemistry: The Central Science 13
For each element, indicate the number of valence electrons, core electrons, and unpaired electrons in the ground state: (a) nitrogen, (b) silicon, (c) chlorine.

Chapter: Problem: 6.75

Chemistry: The Central Science 13
Write the condensed electron configurations for the following atoms, using the appropriate noble-gas core abbreviations: (a) Cs, (b) Ni, (c) Se, (d) Cd, (e) U, (f) Pb

Chapter: Problem: 6.76

Chemistry: The Central Science 13
Write the condensed electron configurations for the following atoms and indicate how many unpaired electrons each has: (a) Mg, (b) Ge, (c) Br, (d) V, (e) Y, (f) Lu.

Chapter: Problem: 6.77

Chemistry: The Central Science 13
Identify the specific element that corresponds to each of the following electron configurations and indicate the number of unpaired electrons for each: (a) 1s 2 2s 2 , (b) 1s 2 2s 2 2p4 , (c) 3Ar44s 1 3d5 , (d) 3Kr45s 2 4d10 5p4 .

Chapter: Problem: 6.78

Chemistry: The Central Science 13
Identify the group of elements that corresponds to each of the following generalized electron configurations and indicate the number of unpaired electrons for each: (a) [noble gas] ns 2 np5 (b) [noble gas] ns 2 1n - 12d2 (c) [noble gas] ns 2 1n - 12d10 np1 (d) [noble gas] ns 2 1n - 22f 6

Chapter: Problem: 6.79

Chemistry: The Central Science 13
What is wrong with the following electron configurations for atoms in their ground states? (a) 1s 2 2s 2 3s 1 , (b) 3Ne42s 2 2p3 , (c) 3Ne43s 2 3d5 .

Chapter: Problem: 6.80

Chemistry: The Central Science 13
The following electron configurations represent excited states. Identify the element and write its ground-state condensed electron configuration. (a) 1s 2 2s 2 2p4 3s 1 , (b) 3Ar44s 1 3d10 4p2 5p1 , (c) 3Kr45s 2 4d2 5p1

Chapter: Problem: 6.81

Chemistry: The Central Science 13
Consider the two waves shown here, which we will consider to represent two electromagnetic radiations: (a) What is the wavelength of wave A? Of wave B? (b) What is the frequency of wave A? Of wave B? (c) Identify the regions of the electromagnetic spectrum to which waves A and B belong. A B 1.6 107

Chapter: Problem: 6.82

Chemistry: The Central Science 13
If you put 120 volts of electricity through a pickle, the pickle will smoke and start glowing orange- yellow. The light is emitted because sodium ions in the pickle become excited; their return to the ground state results in light emission. (a) The wavelength of this emitted light is 589 nm. Calculat

Chapter: Problem: 6.83

Chemistry: The Central Science 13
Certain elements emit light of a specific wavelength when they are burned. Historically, chemists used such emission wavelengths to determine whether specific elements were present in a sample. Characteristic wavelengths for some of the elements are given in the following table: Ag 328.1 nm Fe 372.0

Chapter: Problem: 6.84

Chemistry: The Central Science 13
In August 2011, the Juno spacecraft was launched from Earth with the mission of orbiting Jupiter in 2016. The closest distance between Jupiter and Earth is 391 million miles. (a) If it takes 5.0 years for Juno to reach Jupiter, what is its average speed in mi/hr over this period? (b) Once Juno reache

Chapter: Problem: 6.85

Chemistry: The Central Science 13
The rays of the Sun that cause tanning and burning are in the ultraviolet portion of the electromagnetic spectrum. These rays are categorized by wavelength. So-called UV-A radiation has wavelengths in the range of 320380 nm, whereas UV-B radiation has wavelengths in the range of 290320 nm. (a) Calcul

Chapter: Problem: 6.86

Chemistry: The Central Science 13
The watt is the derived SI unit of power, the measure of energy per unit time: 1 W = 1 J>s. A semiconductor laser in a CD player has an output wavelength of 780 nm and a power level of 0.10 mW. How many photons strike the CD surface during the playing of a CD 69 minutes in length?

Chapter: Problem: 6.87

Chemistry: The Central Science 13
Carotenoids are yellow, orange, and red pigments synthesized by plants. The observed color of an object is not the color of light it absorbs but rather the complementary color, as described by a color wheel such as the one shown here. On this wheel, complementary colors are across from each other. (a

Chapter: Problem: 6.88

Chemistry: The Central Science 13
In an experiment to study the photoelectric effect, a scientist measures the kinetic energy of ejected electrons as a function of the frequency of radiation hitting a metal surface. She obtains the following plot. The point labeled n0 corresponds to light with a wavelength of 542 nm. (a) What is the

Chapter: Problem: 6.89

Chemistry: The Central Science 13
Consider a transition in which the hydrogen atom is excited from n = 1 to n = . (a) What is the end result of this transition? (b) What is the wavelength of light that must be absorbed to accomplish this process? (c) What will occur if light with a shorter wavelength than that in part (b) is used to

Chapter: Problem: 6.90

Chemistry: The Central Science 13
The human retina has three types of receptor cones, each sensitive to a different range of wavelengths of visible light, as shown in this figure (the colors are merely to differentiate the three curves from one another; they do not indicate the actual colors represented by each curve): 400 500 600 Wa

Chapter: Problem: 6.91

Chemistry: The Central Science 13
The series of emission lines of the hydrogen atom for which nf = 3 is called the Paschen series. (a) Determine the region of the electromagnetic spectrum in which the lines of the Paschen series are observed. (b) Calculate the wavelengths of the first three lines in the Paschen seriesthose for which

Chapter: Problem: 6.92

Chemistry: The Central Science 13
When the spectrum of light from the Sun is examined in high resolution in an experiment similar to that illustrated in Figure 6.9, dark lines are evident. These are called Fraunhofer lines, after the scientist who studied them extensively in the early nineteenth century. Altogether, about 25,000 line

Chapter: Problem: 6.93

Chemistry: The Central Science 13
Determine whether each of the following sets of quantum numbers for the hydrogen atom are valid. If a set is not valid, indicate which of the quantum numbers has a value that is not valid: (a) n = 4, l = 1, ml = 2, ms = -1 2 (b) n = 4, l = 3, ml = -3, ms = +1 2 (c) n = 3, l = 2, ml = -1, ms = +1 2 (d

Chapter: Problem: 6.94

Chemistry: The Central Science 13
Bohrs model can be used for hydrogen-like ionsions that have only one electron, such as He+ and Li 2 + . (a) Why is the Bohr model applicable to He+ ions but not to neutral He atoms? (b) The ground- state energies of H, He+ , and Li 2 + are tabulated as follows: Atom or ion H he+ Li 2 + Ground-state

Chapter: Problem: 6.95

Chemistry: The Central Science 13
An electron is accelerated through an electric potential to a kinetic energy of 13.4 keV. What is its characteristic wavelength? [Hint: Recall that the kinetic energy of a moving object is E = 1 2 mv2 , where m is the mass of the object and n is the speed of the object.]

Chapter: Problem: 6.96

Chemistry: The Central Science 13
In the television series Star Trek, the transporter beam is a device used to beam down people from the Starship Enterprise to another location, such as the surface of a planet. The writers of the show put a Heisenberg compensator into the transporter beam mechanism. Explain why such a compensator (wh

Chapter: Problem: 6.97

Chemistry: The Central Science 13
As discussed in the A Closer Look box on Measurement and the Uncertainty Principle, the essence of the uncertainty principle is that we cant make a measurement without disturbing the system that we are measuring. (a) Why cant we measure the position of a subatomic particle without disturbing it? (b)

Chapter: Problem: 6.98

Chemistry: The Central Science 13
Consider the discussion of radial probability functions in A Closer Look in Section 6.6. (a) What is the difference between the probability density as a function of r and the radial probability function as a function of r ? (b) What is the significance of the term 4pr 2 in the radial probability func

Chapter: Problem: 6.99

Chemistry: The Central Science 13
For orbitals that are symmetric but not spherical, the contour representations (as in Figures 6.23 and 6.24) suggest where nodal planes exist (that is, where the electron density is zero). For example, the px orbital has a node wherever x = 0. This equation is satisfied by all points on the yz plane,

Chapter: Problem: 6.100

Chemistry: The Central Science 13
The Chemistry and Life box in Section 6.7 described the techniques called NMR and MRI. (a) Instruments for obtaining MRI data are typically labeled with a frequency, such as 600 MHz. Why do you suppose this label is relevant to the experiment? (b) What is the value of E in Figure 6.27 that would corr

Chapter: Problem: 6.101

Chemistry: The Central Science 13
Suppose that the spin quantum number, ms, could have three allowed values instead of two. How would this affect the number of elements in the first four rows of the periodic table?

Chapter: Problem: 6.102

Chemistry: The Central Science 13
Using the periodic table as a guide, write the condensed electron configuration and determine the number of unpaired electrons for the ground state of (a) Br, (b) Ga, (c) Hf, (d) Sb, (e) Bi, (f) Sg

Chapter: Problem: 6.103

Chemistry: The Central Science 13
Scientists have speculated that element 126 might have a moderate stability, allowing it to be synthesized and characterized. Predict what the condensed electron configuration of this element might be.

Chapter: Problem: 6.104

Chemistry: The Central Science 13
In the experiment shown schematically below, a beam of neutral atoms is passed through a magnetic field. Atoms that have unpaired electrons are deflected in different directions in the magnetic field depending on the value of the electron spin quantum number. In the experiment illustrated, we envisio

Chapter: Problem: 6.105

Chemistry: The Central Science 13
Microwave ovens use microwave radiation to heat food. The energy of the microwaves is absorbed by water molecules in food and then transferred to other components of the food. (a) Suppose that the microwave radiation has a wavelength of 11.2 cm. How many photons are required to heat 200 mL of coffee

Chapter: Problem: 6.106

Chemistry: The Central Science 13
The stratospheric ozone 1O32 layer helps to protect us from harmful ultraviolet radiation. It does so by absorbing ultraviolet light and falling apart into an O2 molecule and an oxygen atom, a process known as photodissociation. O31g2 O21g2 + O1g2 Use the data in Appendix C to calculate the enthalpy

Chapter: Problem: 6.107

Chemistry: The Central Science 13
The discovery of hafnium, element number 72, provided a controversial episode in chemistry. G. Urbain, a French chemist, claimed in 1911 to have isolated an element number 72 from a sample of rare earth (elements 5871) compounds. However, Niels Bohr believed that hafnium was more likely to be found a

Chapter: Problem: 6.108a

Chemistry: The Central Science 13
(a) Account for formation of the following series of oxides in terms of the electron configurations of the elements and the discussion of ionic compounds in Section 2.7: K2O, CaO, Sc2O3, TiO2, V2O5, CrO3.

Chapter: Problem: 6.108b

Chemistry: The Central Science 13
(b) Name these oxides.

Chapter: Problem: 6.108c

Chemistry: The Central Science 13
(c) Consider the metal oxides whose enthalpies of formation (in kJ mol - 1 ) are listed here. Oxide K2o1s2 Cao1s2 Tio21s2 V2o51s2 Hf -363.2 -635.1 -938.7 -1550.6 Calculate the enthalpy changes in the following general reaction for each case: MnOm1s2 + H21g2 nM1s2 + mH2O1g2 (You will need to write the

Chapter: Problem: 6.108d

Chemistry: The Central Science 13
(d) Based on the data given, estimate a value of Hf for Sc2O31s2.

Chapter: Problem: 6.109

Chemistry: The Central Science 13
The first 25 years of the twentieth century were momentous for the rapid pace of change in scientists understanding of the nature of matter. (a) How did Rutherfords experiments on the scattering of a particles by a gold foil set the stage for Bohrs theory of the hydrogen atom? (b) In what ways is de

Chapter: Problem: 6.110

Chemistry: The Central Science 13
The two most common isotopes of uranium are 235 U and 238 U. (a) Compare the number of protons, the number of electrons, and the number of neutrons in atoms of these two isotopes. (b) Using the periodic table in the front-inside cover, write the electron configuration for a U atom. (c) Compare your a

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