Chemistry: The Central Science 12th Edition solutions

Chemistry: The Central Science 12
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

Chemistry: The Central Science 12
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

Chemistry: The Central Science 12
The following diagrams represent two electromagnetic waves. Which wave corresponds to the higher-energy radiation? Explain.[Section 6.2]

Chemistry: The Central Science 12
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 fundam

Chemistry: The Central Science 12
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

Chemistry: The Central Science 12
A certain quantum mechanical system has the energy levels shown in the diagram below.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 involved

Chemistry: The Central Science 12
Consider a fictitious one-dimensional system with one electron. The wave function for the electron, drawn at the top of the next page, is from to . (a) Sketch the probability density, , from to . (b)At what value or values of x will there be the greatest probability of finding the electron? (c) What

Chemistry: The Central Science 12
The contour representation of one of the orbitals for the shell of a hydrogen atom is shown below. (a) What is the quantum number l for this orbital? (b) How do we label this orbital? (c)How would you modify this sketch to show the analogous orbital for the shell? [Section 6.6]

Chemistry: The Central Science 12
The drawing below 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]

Chemistry: The Central Science 12
State where in the periodic table these elements appear: (a) elements with the valence-shell electron configuration (b) elements that have three unpaired p electrons (c) an element whose valence electrons are (d) the d-block elements

Chemistry: The Central Science 12
What are the basic SI units for (a) the wavelength of light, (b) the frequency of light,(c) the speed of light?

Chemistry: The Central Science 12
(a) What is the relationship between the wavelength and the frequency of radiant energy? (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?

Chemistry: The Central Science 12
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

Chemistry: The Central Science 12
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

Chemistry: The Central Science 12
Arrange the following kinds of electromagnetic radiation in order of increasing wavelength: infrared,green light,red light, radio waves,X-rays,ultraviolet light.

Chemistry: The Central Science 12
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)

Chemistry: The Central Science 12
(a)What is the frequency of radiation that has a wavelength of , about the size of a bacterium? (b) What is the wavelength of radiation that has a frequency of ? (c)Would the radiations in part (a) or part (b) be visible to the human eye? (d)What distance does electromagnetic radiation travel in ?

Chemistry: The Central Science 12
(a) What is the frequency of radiation whose wavelength is \(5.0 \times 10^{-5} \mathrm{m}\)? (b) What is the wavelength of radiation that has a frequency of \(2.5 \times 10^{8} \mathrm{s}^{-1}\)? (c) Would the radiations in part (a) or part (b) be detected by an X-ray detector? (d) What distance doe

Chemistry: The Central Science 12
An argon ion laser emits light at 532 nm. What is the frequency of this radiation? Using Figure 6.4, predict the color associated with this wavelength.

Chemistry: The Central Science 12
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?

Chemistry: The Central Science 12
If human height were quantized in one-foot increments,what would happen to the height of a child as she grows up?

Chemistry: The Central Science 12
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.

Chemistry: The Central Science 12
(a) Calculate the energy of a photon of electromagnetic radiation whose frequency is .(b) Calculate the energy of a photon of radiation whose wavelength is 322 nm.(c) What wavelength of radiation has photons of energy

Chemistry: The Central Science 12
(a)A red laser pointer emits light with a wavelength of 650 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) from their ground state to an upper excited state. When t

Chemistry: The Central Science 12
(a) Calculate and compare the energy of a photon of wavelength with that of wavelength 0.154 nm. (b) Use Figure 6.4 to identify the region of the electromagnetic spectrum to which each belongs.

Chemistry: The Central Science 12
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.

Chemistry: The Central Science 12
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 b

Chemistry: The Central Science 12
The energy from radiation can be used to cause the rupture of chemical bonds.A minimum energy of is required to break the nitrogennitrogen bond in . What is the longest wavelength of radiation that possesses the necessary energy to break the bond? What type of electromagnetic radiation is this?

Chemistry: The Central Science 12
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?

Chemistry: The Central Science 12
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 per second at this wavelength, what is the total energy of the photons detected in one hour?

Chemistry: The Central Science 12
Molybdenum metal must absorb radiation with a minimum frequency of 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 molybdenum is irra

Chemistry: The Central Science 12
Sodium metal requires a photon with a minimum energy of to emit electrons. (a) What is the minimum frequency of light necessary to emit electrons from sodium via the photoelectric effect? (b) What is the wavelength of this light? (c) If sodium is irradiated with light of 405 nm, what is the maximum p

Chemistry: The Central Science 12
Explain how the existence of line spectra is consistent with Bohrs theory of quantized energies for the electron in the hydrogen atom.

Chemistry: The Central Science 12
(a) In terms of the Bohr theory of the hydrogen atom, what process is occurring when excited hydrogen atoms emit radiant energy of certain wavelengths and only those wavelengths? (b) Does a hydrogen atom expandor contractas it moves from its ground state to an excited state?

Chemistry: The Central Science 12
Is energy emitted or absorbed when the following electronic transitions occur in hydrogen: (a) from to , (b) from an orbit of radius to one of radius , (c)an electron adds to the ion and ends up in the shell?

Chemistry: The Central Science 12
Indicate whether energy is emitted or absorbed when the following electronic transitions occur in hydrogen: (a) from to , (b) from an orbit of radius 4.76 to one of radius ,(c) from the to the state.

Chemistry: The Central Science 12
(a) Using Equation 6.5, calculate the energy of an electron in the hydrogen atom when and when . Calculate the wavelength of the radiation released when an electron moves from to . (b) Is this line in the visible region of the electromagnetic spectrum? If so, what color is it?

Chemistry: The Central Science 12
(a) Calculate the energies of an electron in the hydrogen atom for and for . How much energy does it require to move the electron out of the atom completely (from to ), according to Bohr? Put your answer in . (b) The energy for the process is called the ionization energy of hydrogen. The experimental

Chemistry: The Central Science 12
The visible emission lines observed by Balmer all involved . (a) Explain why only the lines with were observed in the visible region of the electromagnetic spectrum. (b) Calculate the wavelengths of the first three lines in the Balmer seriesthose for which ,and 5and identify these lines in the emissi

Chemistry: The Central Science 12
The Lyman series of emission lines of the hydrogen atom are those for which . (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 lines in the Lyman seriesthose for which , and 4.

Chemistry: The Central Science 12
One of the emission lines of the hydrogen atom has a wavelength of 93.8 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.

Chemistry: The Central Science 12
The hydrogen atom can absorb light of wavelength 2626 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.

Chemistry: The Central Science 12
Use the de Broglie relationship to determine the wavelengths of the following objects: (a) an 85-kg person skiing at , (b) a 10.0-g bullet fired at , (c) a lithium atom moving at , (d) an ozone molecule in the upper atmosphere moving at .

Chemistry: The Central Science 12
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 a velocity of .

Chemistry: The Central Science 12
Neutron diffraction is an important technique for determining the structures of molecules. Calculate the velocity of a neutron needed to achieve a wavelength of . (Refer to the inside cover for the mass of the neutron).

Chemistry: The Central Science 12
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 . What is the characteristic wavelength of this electron? Is the wavelength comparable

Chemistry: The Central Science 12
Using Heisenbergs uncertainty principle, calculate the uncertainty in the position of (a) a 1.50-mg mosquito moving at a speed of if the speed is known to within ; (b) a proton moving at a speed of . (The mass of a proton is given in the table of fundamental constants in the inside cover of the text.

Chemistry: The Central Science 12
Calculate the uncertainty in the position of (a) an electron moving at a speed of , (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)What are the implications of these calculations to

Chemistry: The Central Science 12
(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 Broglies hypothesis? (c) What is meant by the term probability density? Given the wave function, how do we find the probability

Chemistry: The Central Science 12
(a) According to the Bohr model, an electron in the ground state of a hydrogen atom orbits the nucleus at a specific radius of . 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 different? (b)

Chemistry: The Central Science 12
(a) For ,what are the possible values of l ? (b) For , what are the possible values of ? (c) If is 2, what are the possible values for l ?

Chemistry: The Central Science 12
How many possible values for l and are there when (a) ; (b) ?

Chemistry: The Central Science 12
Give the numerical values of n and l corresponding to each of the following orbital designations:(a)3p, (b)2s,(c)4f,(d)5d.

Chemistry: The Central Science 12
Give the values for n, l, and for (a) each orbital in the 2p subshell,(b) each orbital in the 5d subshell.

Chemistry: The Central Science 12
Which of the following represent impossible combinations of n and l: (a) 1p, (b) 4s, (c) 5f, (d) 2d?

Chemistry: The Central Science 12
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.

Chemistry: The Central Science 12
Sketch the shape and orientation of the following types of orbitals: (a) s, (b) ,(c) .

Chemistry: The Central Science 12
Sketch the shape and orientation of the following types of orbitals: (a) ,(b) ,(c) .

Chemistry: The Central Science 12
(a) What are the similarities and differences between the 1s and 2sorbitals of the hydrogen atom? (b)In what sense does a 2porbital have directional character? Compare the directionalcharacteristics ofthe and orbitals.(That is,in what direction or region ofspace is the electron density concentrated?)

Chemistry: The Central Science 12
(a) With reference to Figure 6.18, 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 orbital; in the 3s orbital.(c) What information i

Chemistry: The Central Science 12
For a given value of the principal quantum number,n, how do the energies of the s,p,d,andfsubshells vary for (a)hydrogen, (b) a many-electron atom?

Chemistry: The Central Science 12
(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 energy to remove a 3selectron from the chlorine atom,as compared with a 2pelect

Chemistry: The Central Science 12
(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) Draw an arrow showing the excitation of an electron from the 1s to the 2s orbi

Chemistry: The Central Science 12
(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.Explain.

Chemistry: The Central Science 12
What is the maximum number of electrons that can occupy each of the following subshells: (a) 3p, (b) 5d, (c) 2s, (d) 4f ?

Chemistry: The Central Science 12
What is the maximum number of electrons in an atom that can have the following quantum numbers: (a) , , (b) ,; (c) , , ; (d) ?

Chemistry: The Central Science 12
(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?

Chemistry: The Central Science 12
For each element, indicate the number of valence electrons, core electrons, and unpaired electrons in the ground state: (a) carbon,(b) phosphorus,(c) neon.

Chemistry: The Central Science 12
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.

Chemistry: The Central Science 12
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.

Chemistry: The Central Science 12
Identify the specific element that corresponds to each of the following electron configurations and indicate the number of unpaired electrons for each: (a) , (b) , (c) ,(d) .

Chemistry: The Central Science 12
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] (b) [noble gas] (c) [noble gas] (d) [noble gas]

Chemistry: The Central Science 12
What is wrong with the following electron configurations for atoms in their ground states? (a) , (b) , (c) .

Chemistry: The Central Science 12
The following electron configurations represent excited states. Identify the element, and write its ground-state condensed electron configuration.(a) ,(b) , (c) .

Chemistry: The Central Science 12
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.

Chemistry: The Central Science 12
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 i

Chemistry: The Central Science 12
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 which el

Chemistry: The Central Science 12
In June 2004, the CassiniHuygens spacecraft began orbiting Saturn and transmitting images to Earth. The closest distance between Saturn and Earth is 746 million miles. What is the minimum amount of time it takes for the transmitted signals to travel from the spacecraft to Earth?

Chemistry: The Central Science 12
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

Chemistry: The Central Science 12
The watt is the derived SI unit of power,the measure of energy per unit time: . 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?

Chemistry: The Central Science 12
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)

Chemistry: The Central Science 12
A photocell is a device used to measure the intensity of light. In a certain experiment, when light of wavelength 630 nm is directed onto the photocell,electrons are emitted at the rate of (coulombs per second). Assume that each photon that impinges on the photocell emits one electron. How many photo

Chemistry: The Central Science 12
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 corresponds to light with a wavelength of 680 nm. (a) What is the val

Chemistry: The Central Science 12
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) Estimate the

Chemistry: The Central Science 12
The series of emission lines of the hydrogen atom for which 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 ,and 6.

Chemistry: The Central Science 12
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

Chemistry: The Central Science 12
Bohrs model can be used for hydrogen-like ionsions that have only one electron, such as and . (a) Why is the Bohr model applicable to ions but not to neutral He atoms? (b) The ground-state energies of H, , and are tabulated as follows: By examining these numbers, propose a relationship between the g

Chemistry: The Central Science 12
An electron is accelerated through an electric potential to a kinetic energy of 18.6 keV. What is its characteristic wavelength? [Hint: Recall that the kinetic energy of a moving object is \(E=\frac{1}{2} m v^{2}\), where m is the mass of the object and is the speed of the object.]

Chemistry: The Central Science 12
In the television series Star Trek, the transporter beam is a device used to beam downpeople 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 (which

Chemistry: The Central Science 12
Which of the quantum numbers governs (a) the shape of an orbital, (b) the energy of an orbital, (c) the spin properties of the electron,(d) the spatial orientation of the orbital?

Chemistry: The Central Science 12
Consider the discussion of radial probability functions in A Closer Lookin 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 in the radial probability functions for

Chemistry: The Central Science 12
For orbitals that are symmetric but not spherical, the contour representations (as in Figures 6.22 and 6.23) suggest where nodal planes exist (that is, where the electron density is zero). For example, the orbital has a node wherever . This equation is satisfied by all points on the yz plane,so this

Chemistry: The Central Science 12
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 in Figure 6.27 that would corresp

Chemistry: The Central Science 12
Suppose that the spin quantum number, , 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?

Chemistry: The Central Science 12
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) Si, (b) Zn, (c) Zr, (d) Sn, (e) Ba,(f) Tl.

Chemistry: The Central Science 12
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.

Chemistry: The Central Science 12
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

Chemistry: The Central Science 12
The stratospheric ozone layer helps to protect us from harmful ultraviolet radiation.It does so by absorbing ultraviolet light and falling apart into an molecule and an oxygen atom,a process known as photodissociation. Use the data in Appendix C to calculate the enthalpy change for this reaction. Wh

Chemistry: The Central Science 12
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 al

Chemistry: The Central Science 12
(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: , CaO, ,,,. (b) Name these oxides.(c) Consider the metal oxides whose enthalpies of formation (in ) are listed here. Calculate the

Chemistry: The Central Science 12
The first 25 years of the twentieth century were momentous for the rapid pace of change in scientistsunderstanding of the nature of matter.(a)How did Rutherfords experiments on the scattering of particles by a gold foil set the stage for Bohrs theory of the hydrogen atom? (b) In what ways is de Brog

Chemistry: The Central Science 12
The two most common isotopes of uranium are and . (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 answer to part

Chemistry: The Central Science 12
Imagine sunlight falling on three square areas. One is an inert black material.The second is a photovoltaic cell surface,which converts radiant energy into electricity.The third is an area on a green tree leaf.Draw diagrams that show the energy conversions in each case, using Figure 5.9 as a model. H