Chemistry

Chemistry: The Central Science | 14th Edition | ISBN: 9780134414232 | Authors: Theodore E. Brown; H. Eugene LeMay; Bruce E. Bursten; Catherine Murphy; Patrick Woodward; Matthew E. Stoltzfus
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Chemistry: The Central Science 14th Edition solutions

Author: Theodore E. Brown; H. Eugene LeMay; Bruce E. Bursten; Catherine Murphy; Patrick Woodward; Matthew E. Stoltzfus
Publisher: Pearson
ISBN: 9780134414232

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Chapter 6 Problems

Chapter: 6 Problem: 6.47

Chemistry: The Central Science 14
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 \(2.5 \times 10^{5} \mathrm{~m} / \mathrm{s}\), (d) an ozone \(\left(\mathrm{O}_{3}\righ

Chapter: 6 Problem: 6.48

Chemistry: The Central Science 14
Among the elementary subatomic particles of physics is the muon, which decays within a few microseconds 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 \(8.85 \times 10^{5} \mathrm{~cm} / \mathrm{s}\).

Chapter: 6 Problem: 6.49

Chemistry: The Central Science 14
Neutron diffraction is an important technique for determining the structures of molecules. Calculate the velocity of a neutron needed to achieve a wavelength of \(1.25 \AA\). (Refer to the inside cover for the mass of the neutron.)

Chapter: 6 Problem: 6.50

Chemistry: The Central Science 14
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 \(9.47 \times 10^{6} \mathrm{~m} / \mathrm{s}\). What is the characteristic wavelength

Chapter: 6 Problem: 6.51

Chemistry: The Central Science 14
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 \(\pm 0.01 \mathrm{~m} / \mathrm{s}\); (b) a proton moving at a speed of \((5.00 \pm 0.01) \times 10^{4} \mathrm{~m} /

Chapter: 6 Problem: 6.52

Chemistry: The Central Science 14
Calculate the uncertainty in the position of (a) an electron moving at a speed of \((3.00 \pm 0.01) \times 10^{5} \mathrm{~m} / \mathrm{s}\), (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

Chapter: 6 Problem: 6.53

Chemistry: The Central Science 14
Classify the following statements as either true or false: (a) In a contour representation of an orbital, such as the one shown here for a 2p orbital, the electron is confined to move about the nucleus on the outer surface of the shape. (b) The probability density \([\psi f(r)]^{2}\) gives

Chapter: 6 Problem: 6.54

Chemistry: The Central Science 14
The radial probability function for a 2s orbital is shown here. Classify the following statements as either true or false: (a) There are two maxima in this function because one electron spends most of its time at an approximate distance of \(0.5 \AA\) from the

Chapter: 6 Problem: 6.55

Chemistry: The Central Science 14
(a) For n = 4, what are the possible values of l? (b) For l = 2, what are the possible values of \(m_{l}\)? (c) If \(m_{l}\) is 2, what are the possible values for l? Text Transcription: m_{l}

Chapter: 6 Problem: 6.56

Chemistry: The Central Science 14
How many unique combinations of the quantum numbers l and \(m_{l}\) are there when (a) n = 3, (b) n = 4? Text Transcription: m_{l}

Chapter: 6 Problem: 6.82

Chemistry: The Central Science 14
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. Calcula

Chapter: 6 Problem: 6.57

Chemistry: The Central Science 14
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: 6 Problem: 6.84

Chemistry: The Central Science 14
In August 2011, the Juno spacecraft was launched from Earth with the mission of orbiting Jupiter, arriving nearly five years later in July of 2016. The distance between the two planets varies depending on where each planet is in its orbit, but at the closest, the distance between Jupiter and Earth is

Chapter: 6 Problem: 6.58

Chemistry: The Central Science 14
Give the values for n, l, and ml for (a) each orbital in the 2p subshell, (b) each orbital in the 5d subshell.

Chapter: 6 Problem: 6.85

Chemistry: The Central Science 14
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) Calc

Chapter: 6 Problem: 6.59

Chemistry: The Central Science 14
A certain orbital of the hydrogen atom has n = 4 and l = 2. (a) What are the possible values of \(m_{l}\) for this orbital? (b) What are the possible values of \(m_{S}\) for the orbital? Text Transcription: m_{S} m_

Chapter: 6 Problem: 6.86

Chemistry: The Central Science 14
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: 6 Problem: 6.60

Chemistry: The Central Science 14
A hydrogen atom orbital has n = 5 and \(m_{l}\) = -2. (a) What are the possible values of l for this orbital? (b) What are the possible values of \(m_{S}\) for the orbital? Text Transcription: m_{S} m_{l}

Chapter: 6 Problem: 6.92

Chemistry: The Central Science 14
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: 6 Problem: 6.61

Chemistry: The Central Science 14
Which of the following represent impossible combinations of n and l? (a) 1p, (b) 4s, (c) 5f, (d) 2d

Chapter: 6 Problem: 6.96

Chemistry: The Central Science 14
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: 6 Problem: 6.62

Chemistry: The Central Science 14
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.

Chapter: 6 Problem: 6.97

Chemistry: The Central Science 14
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?

Chapter: 6 Problem: 6.63

Chemistry: The Central Science 14
Sketch the shape and orientation of the following types of orbitals: (a) s, (b) \(p_{z}\), (c) \(d_{x y}\) Text Transcription: p_{z} d_{x y}

Chapter: 6 Problem: 6.100

Chemistry: The Central Science 14
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. In what region of the electromagnetic spectrum does a photon with this frequency belong? (b) What is the value of

Chapter: 6 Problem: 6.64

Chemistry: The Central Science 14
Sketch the shape and orientation of the following types of orbitals: (a) \(p_{x}\), (b) \(d_{z^{2}}\), (c) \(d_{x^{2}-y^{2}}\). Text Transcription: p_x, d_z2, d_x2 - y2

Chapter: 6 Problem: 6.102

Chemistry: The Central Science 14
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: 6 Problem: 6.65

Chemistry: The Central Science 14
(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 \(p_{x}\) and \(d_{x^{2}-y^{2}}\) orbitals. (That is, in what direction or region o

Chapter: 6 Problem: 6.103

Chemistry: The Central Science 14
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: 6 Problem: 6.66

Chemistry: The Central Science 14
(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 3s orbital.

Chapter: 6 Problem: 6.105

Chemistry: The Central Science 14
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 coffe

Chapter: 6 Problem: 6.67

Chemistry: The Central Science 14
(a) For an \(\mathrm{He}^{+}\) ion, do the 2s and 2p orbitals have the same energy? If not, which orbital has a lower energy? (b) If we add one electron to form the He atom, would your answer to part (a) change? Text T

Chapter: 6 Problem: 6.109

Chemistry: The Central Science 14
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 Bohrs theory of the hydrogen atom? (b) In what ways is d

Chapter: 6 Problem: 6.68

Chemistry: The Central Science 14
(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 3s electron from the chlorine atom, as compared with a

Chapter: 6 Problem: 6.69

Chemistry: The Central Science 14
Two possible electron configurations for an Li atom are shown here. (a) Does either configuration violate the Pauli exclusion principle? (b) Does either configuration violate Hunds rule? (c) In the absence of an external magnetic field, can we say that one electron configuration has a

Chapter: 6 Problem: 6.70

Chemistry: The Central Science 14
An experiment called the SternGerlach experiment helped establish the existence of electron spin. In this experiment, a beam of silver atoms is passed through a magnetic field, which deflects half of the silver atoms in one direction and half in the opposite direction. The separation between the two

Chapter: 6 Problem: 6.71

Chemistry: The Central Science 14
What is the maximum number of electrons that can occupy each of the following subshells? (a) 3p, (b) 5d, (c) 2s, (d) 4f.

Chapter: 6 Problem: 6.72

Chemistry: The Central Science 14
What is the maximum number of electrons in an atom that can have the following quantum numbers? (a) n = 3, \(m_{l}\) = -2; (b) n = 4, l = 3; (c) n = 5, l = 3, \(m_{l}\) = 2; (d) n = 4, l = 1, \(m_{l}\) = 0. Text Transcript

Chapter: 6 Problem: 6.73

Chemistry: The Central Science 14
(a) What are valence electrons? (b) What are core electrons? (c) What does each box in an orbital diagram represent? (d) What object is represented by the half arrows in an orbital diagram? What does the direction of the arrow signify?

Chapter: 6 Problem: 6.74

Chemistry: The Central Science 14
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: 6 Problem: 6.75

Chemistry: The Central Science 14
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: 6 Problem: 6.1

Chemistry: The Central Science 14
The speed of sound in dry air at \(20^{\circ} \mathrm{C}\) is 343 m/s and the lowest frequency sound wave that the human ear can detect is approximately 20 Hz. (a) What is the wavelength of such a sound wave? (b) What would be the frequency of electromagnetic radiation with the same wavelen

Chapter: 6 Problem: 6.76

Chemistry: The Central Science 14
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: 6 Problem: 6.2

Chemistry: The Central Science 14
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 radi

Chapter: 6 Problem: 6.77

Chemistry: The Central Science 14
Identify the specific element that corresponds to each of the following electron configurations and indicate the number of unpaired electrons for each: (a) \(1 s^{2} 2 s^{2}\), (b) \(1 s^{2} 2 s^{2} 2 p^{4}\), (c) \([\mathrm{Ar}] 4 s^{1} 3 d^{5}\), (d) \([\mathrm{Kr}] 5 s^{2} 4 d^{

Chapter: 6 Problem: 6.3

Chemistry: The Central Science 14
The following diagrams represent two electromagnetic waves, drawn on the same scale. (a) Which wave has a longer wavelength? (b) Which wave has a higher frequency? (c) Which wave has a higher energy? [Section 6.2]

Chapter: 6 Problem: 6.78

Chemistry: The Central Science 14
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] \(n s^{2} n p^{5}\) (b) [ noble gas ] \(n s^{2}(n-1) d^{2}\) (c) [noble gas] \(n s^{2}(n-1) d^{10} n p^{1}\)

Chapter: 6 Problem: 6.4

Chemistry: The Central Science 14
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 classi

Chapter: 6 Problem: 6.79

Chemistry: The Central Science 14
The following do not represent valid ground-state electron configurations for an atom either because they violate the Pauli exclusion principle or because orbitals are not filled in order of increasing energy. Indicate which of these two principles is violated in each example. (a) \(1 s^{2} 2 s^

Chapter: 6 Problem: 6.5

Chemistry: The Central Science 14
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? [S

Chapter: 6 Problem: 6.80

Chemistry: The Central Science 14
The following electron configurations represent excited states. Identify the element and write its ground-state condensed electron configuration. (a) \(1 s^{2} 2 s^{2} 2 p^{4} 3 s^{1}\), (b) \([\mathrm{Ar}] 4 s^{1} 3 d^{10} 4 p^{2} 5 p^{1}\), (c) \([\mathrm{Kr}] 5 s^{2} 4 d^{2} 5 p^{1}

Chapter: 6 Problem: 6.6

Chemistry: The Central Science 14
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 num

Chapter: 6 Problem: 6.7

Chemistry: The Central Science 14
Consider the three electronic transitions in a hydrogen atom shown here, labeled A, B, and C. (a) Three electromagnetic waves, all drawn on the same scale, are also shown. Each corresponds to one of the transitions. Which electromagnetic wave (i), (ii), or (iii), is associated with electronic tr

Chapter: 6 Problem: 6.8

Chemistry: The Central Science 14
Consider a fictitious one-dimensional system with one electron. The wave function for the electron, drawn below, is \(\psi(x)=\sin x\) from x = 0 to \(x=2 \pi\). (a) Sketch the probability density, \(\psi^{2}(x)\), from x = 0 to \(x=2 \pi\). (b) At what value or values of x will there be th

Chapter: 6 Problem: 6.9

Chemistry: The Central Science 14
The contour representation of one of the orbitals for the n = 3 shell of a hydrogen atom is shown here. (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 if the value of the magnetic quan

Chapter: 6 Problem: 6.10

Chemistry: The Central Science 14
The accompanying drawing shows a contour plot for a \(d_{y z}\) orbital. Consider the quantum numbers that could potentially correspond to this orbital. (a) What is the smallest possible value of the principal quantum number, n? (b) What is the value of the angular momentum quantum number,

Chapter: 6 Problem: 6.11

Chemistry: The Central Science 14
Four possible electron configurations for a nitrogen atom are shown below, but only one schematic represents the correct configuration for a nitrogen atom in its ground state. Which one is the correct electron configuration? Which configurations violate the Pauli exclusion principle? Which configurat

Chapter: 6 Problem: 6.12

Chemistry: The Central Science 14
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-block elements [Section

Chapter: 6 Problem: 6.13

Chemistry: The Central Science 14
What are the basic SI units for (a) the wavelength of light, (b) the frequency of light, (c) the speed of light?

Chapter: 6 Problem: 6.14

Chemistry: The Central Science 14
(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?

Chapter: 6 Problem: 6.15

Chemistry: The Central Science 14
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) Electr

Chapter: 6 Problem: 6.16

Chemistry: The Central Science 14
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

Chapter: 6 Problem: 6.17

Chemistry: The Central Science 14
Arrange the following kinds of electromagnetic radiation in order of increasing wavelength: infrared, green light, red light, radio waves, X rays, ultraviolet light.

Chapter: 6 Problem: 6.18

Chemistry: The Central Science 14
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

Chapter: 6 Problem: 6.19

Chemistry: The Central Science 14
(a) What is the frequency of radiation that has a wavelength of \(10 \mu \mathrm{m}\), about the size of a bacterium? (b) What is the wavelength of radiation that has a frequency of \(5.50 \times 10^{14} \mathrm{~s}^{-1}\)? (c) Would the radiations in part (a) or part (b) be visible to the

Chapter: 6 Problem: 6.20

Chemistry: The Central Science 14
(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 \(6.4 \times 10^{11} \mathrm{~s}^{-1}\)? (c) Would the radiations in part (a) or part (b) be detected by an X-ray detector? (d) What distance does electro

Chapter: 6 Problem: 6.21

Chemistry: The Central Science 14
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: 6 Problem: 6.22

Chemistry: The Central Science 14
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: 6 Problem: 6.23

Chemistry: The Central Science 14
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

Chapter: 6 Problem: 6.24

Chemistry: The Central Science 14
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: 6 Problem: 6.25

Chemistry: The Central Science 14
(a) Calculate the energy of a photon of electromagnetic radiation whose frequency is \(2.94 \times 10^{14} \mathrm{~s}^{-1}\). (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 \times 10^{-19} \mathrm{

Chapter: 6 Problem: 6.26

Chemistry: The Central Science 14
(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) from their ground state to an upper excited

Chapter: 6 Problem: 6.27

Chemistry: The Central Science 14
(a) Calculate and compare the energy of a photon of wavelength \(3.3 \mu \mathrm{m}\) with that of wavelength 0.154 nm. (b) Use Figure 6.4 to identify the region of the electromagnetic spectrum to which each belongs. T

Chapter: 6 Problem: 6.28

Chemistry: The Central Science 14
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: 6 Problem: 6.29

Chemistry: The Central Science 14
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

Chapter: 6 Problem: 6.30

Chemistry: The Central Science 14
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 \(\mathrm{Cl}_{2}\). What is the longest wavelength of radiation that possesses the necessary energy to break the bond? What type of electroma

Chapter: 6 Problem: 6.31

Chemistry: The Central Science 14
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 t

Chapter: 6 Problem: 6.32

Chemistry: The Central Science 14
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 \(3.2 \times 10^{8}\) photons per second at this wavelength, what is the total energy of the photons detected in 1.0 hour?

Chapter: 6 Problem: 6.33

Chemistry: The Central Science 14
Molybdenum metal must absorb radiation with a minimum frequency of \(1.09 \times 10^{15} \mathrm{~s}^{-1}\) 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 provid

Chapter: 6 Problem: 6.34

Chemistry: The Central Science 14
Titanium metal requires a photon with a minimum energy of \(6.94 \times 10^{-19} \mathrm{~J}\) 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 possi

Chapter: 6 Problem: 6.35

Chemistry: The Central Science 14
Does the hydrogen atom expand or contract when an electron is excited from the n = 1 state to the n = 3 state?

Chapter: 6 Problem: 6.36

Chemistry: The Central Science 14
Classify each of the following statements as either true or false: (a) A hydrogen atom in the n = 3 state can emit light at only two specific wavelengths, (b) a hydrogen atom in the n = 2 state is at a lower energy than one in the n = 1 state, and (c) the energy of an emitted photon eq

Chapter: 6 Problem: 6.37

Chemistry: The Central Science 14
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 \(2.12 \AA\) to one of radius \(8.46 \AA\), (c) an electron adds to the \(\mathrm{H}^{+}\) ion and ends up in the n = 3 shell?

Chapter: 6 Problem: 6.38

Chemistry: The Central Science 14
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 \(4.76 \AA\) to one of radius \(0.529 \AA\), (c) from the n = 6 to the n = 9 state.

Chapter: 6 Problem: 6.39

Chemistry: The Central Science 14
(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. (b) Is this line in the visible region of the electromagnetic spectrum? If so, what color is

Chapter: 6 Problem: 6.40

Chemistry: The Central Science 14
Consider a transition of the electron in the hydrogen atom from n = 4 to n = 9. (a) Is \(\Delta E\) 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 e

Chapter: 6 Problem: 6.41

Chemistry: The Central Science 14
The visible emission lines observed by Balmer all involved \(n_{\mathrm{f}}=2\). (a) Which of the following is the best explanation of why the lines with \(n_{\mathrm{f}}=3\) are not observed in the visible portion of the spectrum: (i) Transitions to \(n_{\mathrm{f}}=3\) are not allowed to

Chapter: 6 Problem: 6.42

Chemistry: The Central Science 14
The Lyman series of emission lines of the hydrogen atom are those for which \(n_{\mathrm{f}}=1\). (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 lines in the Lyman seriesthose for

Chapter: 6 Problem: 6.43

Chemistry: The Central Science 14
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: 6 Problem: 6.44

Chemistry: The Central Science 14
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: 6 Problem: 6.45

Chemistry: The Central Science 14
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: 6 Problem: 6.46

Chemistry: The Central Science 14
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: 6 Problem: 6.81

Chemistry: The Central Science 14
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.

Chapter: 6 Problem: 6.83

Chemistry: The Central Science 14
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) Determi

Chapter: 6 Problem: 6.87

Chemistry: The Central Science 14
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: 6 Problem: 6.88

Chemistry: The Central Science 14
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 0 corresponds to light with a wavelength of 542 nm. (a) What is t

Chapter: 6 Problem: 6.89

Chemistry: The Central Science 14
Consider a transition in which the electron of a hydrogen atom is excited from n = 1 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

Chapter: 6 Problem: 6.90

Chemistry: The Central Science 14
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: 6 Problem: 6.91

Chemistry: The Central Science 14
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 f

Chapter: 6 Problem: 6.93

Chemistry: The Central Science 14
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) \(n=4, l=1, m_{l}=2, m_{s}=-\frac{1}{2}\) (b) \(n=4, l=3, m_{l}=-3, m_{s}=+\frac{1}{2}\) (c) \(n

Chapter: 6 Problem: 6.94

Chemistry: The Central Science 14
Bohrs model can be used for hydrogen-like ionsions that have only one electron, such as He+ and Li2+ . (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 Li2+ are tabulated as follows: By examining these number

Chapter: 6 Problem: 6.95

Chemistry: The Central Science 14
An electron is accelerated through an electric potential to a kinetic energy of 2.15 10-15 J. 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.]

Chapter: 6 Problem: 6.98

Chemistry: The Central Science 14
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 the radial

Chapter: 6 Problem: 6.99

Chemistry: The Central Science 14
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: 6 Problem: 6.101

Chemistry: The Central Science 14
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: 6 Problem: 6.104

Chemistry: The Central Science 14
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: 6 Problem: 6.106

Chemistry: The Central Science 14
The stratospheric ozone (O3) 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. \(\mathrm{O}_{3}(g) \longrightarrow \mathrm{O}_{2}(g)+\mathrm{O}(g)\

Chapter: 6 Problem: 6.107

Chemistry: The Central Science 14
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: 6 Problem: 6.108

Chemistry: The Central Science 14
(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. (b) Name these oxides. (c) Consider the metal oxides whose enthalpies of formation (in k

Chapter: 6 Problem: 6.110

Chemistry: The Central Science 14
The two most common isotopes of uranium are 235U and 238U. (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) Comp

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