Physics

James S. Walker

Chapter 30

Quantum Physics - all with Video Answers

Educators

Chapter Questions

Problem 1

Predict/Explain The blackbody spectrum of blackbody A peaks at a longer wavelength than that of blackbody B. (a) Is the temperature of blackbody A higher than or lower than the temperature of blackbody B? (b) Choose the best explanation from among the following:
I. Blackbody A has the higher temperature because the higher the temperature the longer the wavelength.
II. Blackbody B has the higher temperature because an increase in temperature means an increase in frequency, which corresponds to a decrease in wavelength.

Khoobchandra Agrawal

Khoobchandra Agrawal

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Problem 2

The Surface Temperature of Betelgeuse Betelgeuse, a redgiant star in the constellation Orion, has a peak in its radiation at a frequency of $1.82 \times 10^{14} \mathrm{Hz}$. What is the surface temperature of Betelgeuse?

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Problem 3

What is the frequency of the most intense radiation emitted by your body? Assume a skin temperature of 95 'F. What is the wavelength of this radiation?

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Problem 4

Outer space is filled with a sea of photons, created in the early moments of the universe. The frequency distribution of this "cosmic background radiation" matches that of a blackbody at a temperature near $2.7 \mathrm{K}$. (a) What is the peak frequency of this radiation? (b) What is the wavelength that corresponds to the peak frequency?

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Problem 5

The Sun has a surface temperature of about $5800 \mathrm{K}$. At what frequency does the Sun emit the most radiation?

Prabhat Tyagi

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Problem 6

(a) By what factor does the peak frequency change if the Kelvin temperature of an object is doubled from $20.0 \mathrm{K}$ to $40.0 \mathrm{K}$ ?
(b) By what factor does the peak frequency change if the Celsius temperature of an object is doubled from $20.0^{\circ} \mathrm{C}$ to $40.0^{\circ} \mathrm{C}$ ?

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Problem 7

A Famous Double Star Albireo in the constellation Cygnus, which appears as a single star to the naked eye, is actually a beautiful double-star system. The brighter of the two stars is referred to as A (or Beta-01 Cygni), with a surface temperature of $T_{\Omega}=4700 \mathrm{K} ;$ its companion is $\mathrm{B}$ (or Beta-02 Cygni), with a surface temperature of $T_{\mathrm{B}}=13,000 \mathrm{K}$
(a) When vicwed through a telescope, one star is a brilliant blue color, and the other has a warm golden color, as shown in the accompanying photo. Is the blue star A or B? Explain.
(b) What is the ratio of the peak frequencies emitted by the two stars, $\left(f_{\mathrm{A}} / f_{\mathrm{B}}\right) ?$

Khoobchandra Agrawal

Khoobchandra Agrawal

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Problem 8

Halogen Lightbulbs Modern halogen lightbulbs allow their filaments to operate at a higher temperature than the filaments in standard incandescent bulbs. For comparison, the filament in a standard lightbulb operates at about $2900 \mathrm{K}$ whereas the filament in a halogen bulb may operate at $3400 \mathrm{K}$.
(a) Which bulb has the higher peak frequency? (b) Calculate the ratio of peak frequencies $\left(f_{\text {hal }} / f_{\text {std }}\right)$. (c) The human eye is most sensitive to a frequency around $5.5 \times 10^{14} \mathrm{Hz} .$ Which bulb produces a peak frequency closer to this value?

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Problem 9

A typical lightbulb contains a tungsten filament that reaches a temperature of about $2850 \mathrm{K}$, roughly half the surface temperature of the Sun. (a) Treating the filament as a blackbody, determine the frequency for which its radiation is a maximum.
(b) Do you expect the lightbulb to radiate more energy in the visible or in the infrared part of the spectrum? Explain.

Khoobchandra Agrawal

Khoobchandra Agrawal

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Problem 10

Exciting an Oxygen Molecule An oxygen molecule $\left(\mathrm{O}_{2}\right)$ vibrates with an energy identical to that of a single particle of mass $m=1.340 \times 10^{-26} \mathrm{kg}$ attached to a spring with a force constant of $k=1215 \mathrm{N} / \mathrm{m} .$ The energy levels of the system are uniformly spaced, as indicated in Figure $30-20$, with a separation given by ly . (a) What is the vibration frequency of this molecule?
(b) How much energy must be added to the molecule to excite it from one energy level to the next higher level?

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Problem 11

A source of red light, a source of green light, and a source of blue light each produce beams of light with the same power. Rank these sources in order of increasing
(a) wavelength of light, (b) frequency of light, and (c) number of photons emitted per second. Indicate ties where appropriate.

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Problem 12

Predict/Explain A source of red light has a higher wattage than a source of green light. (a) Is the energy of photons emitted by the red source greater than, less than, or equal to the energy of photons emitted by the green source? (b) Choose the best explanation from among the following:
I. The photons emitted by the red source have the greater energy because that source has the greater wattage.
II. The red-source photons have less energy than the greensource photons because they have a lower frequency. The wattage of the source doesn't matter.
III. Photons from the red source have a lower frequency, but that source also has a greater wattage. The two effects cancel, so the photons have equal energy.

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Problem 13

Predict/Explain A source of yellow light has a higher wattage than a source of blue light. (a) Is the number of photons emitted per second by the yellow source greater than, less than, or equal to the number of photons emitted per second by the blue source? (b) Choose the best explanation from among the following:
I. The yellow source emits more photons per second because
(i) it emits more energy per second than the blue source, and
(ii) its photons have less energy than those of the blue source.
II. The yellow source has the higher wattage, which means its photons have higher energy than the blue-source photons. Therefore, the yellow source emits fewer photons per second.
III. The two sources emit the same number of photons per second because the higher wattage of the yellow source compensates for the higher energy of the blue photons.

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Problem 14

Light of a particular wavelength does not eject electrons from the surface of a given metal.
(a) Should the wavelength of the light be increased or decreased in order to cause electrons to be ejected? (b) Choose the best explanation from among the following:
I. The photons have too little energy to eject electrons. To increase their energy, their wavelength should be increased.
II. The energy of a photon is proportional to its frequency; that is, inversely proportional to its wavelength. To in crease the energy of the photons so they can eject electrons, one must decrease their wavelength.

Khoobchandra Agrawal

Khoobchandra Agrawal

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Problem 15

Light of a particular wavelength and intensity does not eject electrons from the surface of a given metal. Can electrons be ejected from the metal by increasing the intensity of the light? Explain.

Khoobchandra Agrawal

Khoobchandra Agrawal

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Problem 16

When a person visits the local tanning salon, they absorb photons of ultraviolet (UV) light to get the desired tan. What are the frequency and wavelength of a UV photon whose energy is $6.5 \times 10^{-19} \mathrm{J} ?$

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Problem 17

An AM radio station operating at a frequency of $880 \mathrm{kHz}$ radiates $270 \mathrm{kW}$ of power from its antenna. How many photons are emitted by the antenna every second?

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Problem 18

A photon with a wavelength of less than 50.4 nm can ionize a helium atom. What is the ionization potential of helium?

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Problem 19

A flashlight emits $2.5 \mathrm{W}$ of light energy. Assuming a frequency of $5.2 \times 10^{14} \mathrm{Hz}$ for the light, determine the number of photons given off by the flashlight per second.

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Problem 20

Light of frequency $9.95 \times 10^{14} \mathrm{Hz}$ ejects electrons from the surface of silver. If the maximum kinetic energy of the ciected electrons is $0.180 \times 10^{-19} \mathrm{J},$ what is the work function of silver?

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Problem 21

The work function of gold is 4.58 eV. What frequency of light must be used to eject electrons from a gold surface with a maximum kinetic energy of $6.48 \times 10^{-19} \mathrm{J} ?$

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Problem 22

(a) How many 350 -nm (UV) photons are needed to provide a total energy of $2.5 \mathrm{J}$ ?
(b) How many 750 -nm (red) photons are needed to provide the same energy?

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Problem 23

(a) How many photons per second are emitted by a monochromatic lightbulb $(\lambda=650 \mathrm{nm})$ that emits $45 \mathrm{W}$ of power?
(b) If you stand $15 \mathrm{m}$ from this bulb, how many photons enter each of your eyes per second? Assume your pupil is $5.0 \mathrm{mm}$ in diameter and that the bulb radiates uniformly in all directions.

Zulfiqar Ali

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Problem 24

Two $57.5-k W$ radio stations broadcast at different frequencies. Station A broadcasts at a frequency of $892 \mathrm{kHz}$, and station B broadcasts at a frequency of $1410 \mathrm{kHz}$. (a) Which station emits more photons per second? Explain. (b) Which station emits photons of higher energy?

Khoobchandra Agrawal

Khoobchandra Agrawal

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Problem 25

The energy required to separate a hydrogen molecule into its individual atoms is $104.2 \mathrm{kcal}$ per mole of $\mathrm{H}_{2}$, (a) If the dissociation energy $\mathrm{y}$. for a single $\mathrm{H}_{2}$ molecule is provided by one photon, determine its frequency and wavelength. (b) In what region of the electromagnetic spectrum does the photon found in part (a) lie? (Refer to the spectrum shown in Figure $25-8 .)$

Khoobchandra Agrawal

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Problem 26

(a) How many photons are emitted per second by a He-Ne laser that emits $1.0 \mathrm{mW}$ of power at a wavelength $\lambda=632.8 \mathrm{nm} ?$
(b) What is the frequency of the electromagnetic waves emitted by a He-Ne laser?

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Problem 27

You have two lightbulbs of different power and color, as indicated in Figure $30-21$. One is a $150-$ W red bulb, and the other is a $25-\mathrm{W}$ blue bulb. $(a)$ Which bulb emits more photons per second? (b) Which bulb emits photons of higher energy? (c) Calculate the number of photons emitted per second by each bulb. Take $\lambda_{\text {red }}=650 \mathrm{nm}$ and $\lambda_{\text {blue }}=460 \mathrm{nm}$. (Most of the electromagnetic radiation given off by incandescent lightbulbs is in the infrared portion of the spectrum. For the purposes of this problem, however, assume that all of the radiated power is at the wavelengths indicated.)

Khoobchandra Agrawal

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Problem 28

The maximum wavelength an electromagnetic wave can have and still eject an electron from a copper surface is $264 \mathrm{nm}$. What is the work function of a copper surface?

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Problem 29

Aluminum and calcium have photoelectric work functions of $W_{A 1}=4.28 \mathrm{eV}$ and $W_{C a}=2.87 \mathrm{eV}$, respectively.
(a) Which metal requires higher-frequency light to produce photoclectrons? Explain.
(b) Calculate the minimum frequency that will produce photoelectrons from each surface.

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Problem 30

Two beams of light with different wavelengths $\left(\lambda_{A}>\lambda_{B}\right)$ are used to produce photoelectrons from a given metal surface.
(a) Which beam produces photoclectrons with greater kinetic energy? Explain.
(b) Find $K_{\max }$ for cesium $\left(W_{0}=1.9 \mathrm{eV}\right)$ if $\lambda_{A}=620 \mathrm{nm}$ and $\lambda_{B}=410 \mathrm{nm}$

Khoobchandra Agrawal

Khoobchandra Agrawal

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Problem 31

Zinc and cadmium have photoelectric work functions given by $W_{Z n}=4.33 \mathrm{eV}$ and $W_{\mathrm{Cd}}=4.22 \mathrm{eV}$, respectively.
(a) If both metals are illuminated by UV radiation of the same wavelength, which one gives off photoelectrons with the greater maximum kinctic energy? Explain.
(b) Calculate the maximum kinetic energy of photoelectrons from each surface if $\lambda=275 \mathrm{nm}$.

Khoobchandra Agrawal

Khoobchandra Agrawal

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Problem 32

White light, with frequencies ranging from $4.00 \times 10^{14} \mathrm{Hz}$ to $7.90 \times 10^{14} \mathrm{Hz},$ is incident on a potassium surface. Given that the work function of potassium is $2.24 \mathrm{eV}$, find (a) the maximum kinetic energy of electrons ejected from this surface and
(b) the range of frequencies for which no electrons are ejected.

Narayan Hari

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Problem 33

Electromagnetic waves, with frequencies ranging from $4.00 \times 10^{14} \mathrm{Hz}$ to $9.00 \times 10^{16} \mathrm{Hz},$ are incident on an aluminum surface. Given that the work function of aluminum is $4.28 \mathrm{eV}$. find (a) the maximum kinetic energy of electrons ejected from this surface and (b) the range of frequencies for which no electrons are ejected.

Narayan Hari

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Problem 34

Platinum has a work function of $6.35 \mathrm{eV}$, and iron has a a work function of 4.50 eV. Light of frequency $1.88 \times 10^{15} \mathrm{Hz}$ ejects electrons from both of these surfaces.
(a) From which surface will the ejected electrons have a greater maximum kinetic energy? Explain.
(b) Calculate the maximum kinetic energy of ejected electrons for each surface.

Khoobchandra Agrawal

Khoobchandra Agrawal

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Problem 35

When light with a frequency $f_{1}=547.5$ THz illuminates a metal surface, the most energetic photoelectrons have $1.260 \times 10^{-19} \mathrm{J}$ of kinetic energy. When light with a frequency $f_{2}=738.8 \mathrm{TH} z$ is used instead, the most energetic photoelectrons have $2.480 \times 10^{-19} \mathrm{J}$ of kinetic energy. Using these $\mathrm{ex}$ perimental results, determine the approximate value of Planck's constant.

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Problem 36

Owl Vision Owls have large, sensitive eyes for good night vision. Typically, the pupil of an owl's eye can have a diameter of $8.5 \mathrm{mm}$ (as compared with a maximum diameter of about $7.0 \mathrm{mm}$ for humans). In addition, an owl's eye is about 100 times more sensitive to light of low intensity than a human eye, allowing owls to detect light with an intensity as small as $5.0 \times 10^{-13} \mathrm{W} / \mathrm{m}^{2} .$ Find the minimum number of photons per second an owl can detect, assuming a frequency of $7.0 \times 10^{14} \mathrm{Hz}$ for the light.

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Problem 37

If the momentum of a particle with finite mass is doubled, its kinetic energy increases by a factor of $4 .$ If the momentum of a photon is doubled, by what factor does its energy increase?

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Problem 38

The photons used in microwave ovens have a momentum of $5.1 \times 10^{-33} \mathrm{kg} \cdot \mathrm{m} / \mathrm{s}$
(a) What is their wavelength?
(b) How does the wavelength of the microwaves compare with the size of the holes in the metal screen on the door of the oven?

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Problem 39

What speed must an clectron have if its momentum is to be the same as that of an $\mathrm{X}$ -ray photon with a wavelength of $0.25 \mathrm{nm} ?$

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Problem 40

What is the wavelength of a photon that has the same momentum as an electron moving with a speed of $1200 \mathrm{m} / \mathrm{s} ?$

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Problem 41

What is the frequency of a photon that has the same momentum as a neutron moving with a speed of $1500 \mathrm{m} / \mathrm{s}$ ?

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Problem 42

A hydrogen atom, initially at rest, emits an ultraviolet photon with a wavelength of $\lambda=122 \mathrm{nm}$. What is the recoil speed of the atom after emitting the photon?

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Problem 43

A blue-green photon $(\lambda=486 \mathrm{nm})$ is absorbed by a free hydrogen atom, initially at rest. What is the recoil speed of the hydrogen atom after absorbing the photon?

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Problem 44

(a) Which has the greater momentum, a photon of red light or a photon of blue light? Explain. (b) Calculate the momentum of a photon of red light $\left(f=4.0 \times 10^{14} \mathrm{Hz}\right)$ and a photon of blue light $\left(f=7.9 \times 10^{14} \mathrm{Hz}\right)$.

Khoobchandra Agrawal

Khoobchandra Agrawal

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Problem 45

Photon A has twice the momentum of photon B.
(a) Which photon has the greater wavelength? Explain.
(b) If the wave length of photon A is 333 nm, what is the wavelength of photon B?

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Problem 46

A laser produces a 5.00 -mW beam of light, consisting of photons with a wavelength of $632.8 \mathrm{nm}$.
(a) How many photons are emitted by the laser each second? (b) The laser beam strikes a black surface and is absorbed. What is the change in the momentum of each photon that is absorbed?
(c) What force does the laser beam exert on the black surface?

Zulfiqar Ali

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Problem 47

A laser produces a $7.50-\mathrm{mW}$ beam of light, consisting of photons with a wavelength of $632.8 \mathrm{nm}$. (a) How many photons are emitted by the laser each second? (b) The laser beam strikes a mirror at normal incidence and is reflected. What is the change in momentum of each reflected photon? Give the magnitude only, (c) What force does the laser beam exert on the mirror?

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Problem 48

ln a Compton scattering experiment, the scattered electron is observed to move in the same direction as the incident $X$ ray photon. What is the scattering angle of the photon? Explain.

Khoobchandra Agrawal

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Problem 49

An X-ray photon has 38.0 keV of energy before it scatters from a free electron, and 33.5 keV after it scatters. What is the kinetic energy of the recoiling electron?

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Problem 50

In the Compton effect, an $X$ -ray photon scatters from a free electron. Find the change in the photon's wavelength if it scatters at an angle of $(a) \theta=30.0^{\circ}$,
(b) $\theta=90.0^{\circ},$ and
(c) $\theta=180.0^{\circ}$ relative to the incident direction.

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Problem 51

An X-ray scattering from a free electron is observed to change its wavelength by $3.13 \mathrm{pm} . \mathrm{At}$ what angle to the incident direction does the scattered $X$ -ray move?

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Problem 52

The maximum Compton shift in wavelength occurs when a photon is scattered through $180^{\circ}$. What scattering angle will produce a wavelength shift of one-fourth the maximum?

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Problem 52

Consider two different photons that scatter through an angle of $180^{\circ}$ from a free electron. One is a visible-light photon with $\lambda=520 \mathrm{nm},$ the other is an $\mathrm{X}$ -ray photon with $\lambda=0.030 \mathrm{nm} .$ (a) Which (if either) photon experiences the greater change in wavelength as a result of the scattering? Explain.
(b) Which photon experiences the greater percentage change in wavelength? Explain.
(c) Calculate the percentage change in wavelength of each photon.

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 53

Consider two different photons that scatter through an angle of $180^{\circ}$ from a free electron. One is a visible-light photon with $\lambda=520 \mathrm{nm},$ the other is an $\mathrm{X}$ -ray photon with $\lambda=0.030 \mathrm{nm}$
(a) Which (if either) photon experiences the greater change in wavelength as a result of the scattering? Explain. (b) Which photon experiences the greater percentage change in wavelength? Explain.
(c) Calculate the percentage change in wavelength of each photon.

Khoobchandra Agrawal

Khoobchandra Agrawal

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Problem 54

An X-ray photon with a wavelength of 0.240 nm scatters from a free electron at rest. The scattered photon moves at an angle of $105^{\circ}$ relative to its incident direction. Find (a) the initial momentum and (b) the final momentum of the photon.

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Problem 55

An X-ray photon scatters from a free electron at rest at an angle of $175^{\circ}$ relative to the incident direction.
(a) If the scattered photon has a wavelength of $0.320 \mathrm{nm},$ what is the wavelength of the incident photon? (b) Determine the energy of the incident and scattered photons.
(c) Find the kinetic energy of the recoil electron.

Narayan Hari

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Problem 56

An X-ray photon scatters through $180^{\circ}$ from (i) an electron or (ii) a helium atom. (a) In which case is the change in wavelength of the X-ray greater? Explain. (b) Calculate the change in wavelength for each of these two cases.

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Problem 57

A photon has an energy $E$ and wavelength $\lambda$ before scattering from a free electron. After scattering through a $135^{\circ}$ angle, the photon's wavelength has increased by $10.0 \%$. Find the initial wavelength and energy of the photon.

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Problem 58

Find the direction of propagation of the scattered electron in Problem 51 , given that the incident $X$ -ray has a wavelength of $0.525 \mathrm{nm}$ and propagates in the positive $x$ direction.

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 59

(a) As you accelerate your car away from
a stoplight, does the de Broglie wavelength of the car increase, decrease, or stay the same? (b) Choose the best explanation from among the following:
I. The de Broglie wavelength will increase because the momentum of the car has increased.
II. The momentum of the car increases. It follows that the de Broglie wavelength will decrease, because it is inversely proportional to the wavelength.
III. The de Broglie wavelength of the car depends only on its mass, which doesn't change by pulling away from the stoplight. Therefore, the de Broglie wavelength stays the same.

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Problem 60

By what factor does the de Broglie wavelength of a particle change if $(a)$ its momentum is doubled or $(b)$ its kinetic energy is doubled? Assume the particle is nonrelativistic.

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Problem 61

A particle with a mass of $6.69 \times 10^{-27} \mathrm{kg}$ has a de Broglie wavelength of $7.22 \mathrm{pm}$. What is the particle's speed?

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Problem 62

What speed must a neutron have if its de Broglie wavelength is to be equal to the interionic spacing of table salt $(0.282 \mathrm{nm}) ?$

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Problem 63

A $79-\mathrm{kg}$ jogger runs with a speed of $4.2 \mathrm{m} / \mathrm{s}$. If the jogger is considered to be a particle, what is her de Broglie wavelength?

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Problem 64

Find the kinctic energy of an electron whose de Broglie wavelength is 1.5 A.

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Problem 65

A beam of neutrons with a de Broglie wavelength of $0.250 \mathrm{nm}$ diffracts from a crystal of table salt, which has an interionic spacing of $0.282 \mathrm{nm}$
(a) What is the speed of the neutrons?
(b) What is the angle of the second interference maximum?

Zulfiqar Ali

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Problem 66

An electron and a proton have the same speed. (a) Which has the longer de Broglie wavelength? Explain. (b) Calculate the ratio $\left(\lambda_{\mathrm{e}} / \lambda_{\mathrm{p}}\right)$

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Problem 67

An electron and a proton have the same de Broglie wavelength. (a) Which has the greater kinetic energy? Explain. (b) Calculate the ratio of the electron's kinetic energy to the kinetic energy of the proton.

Narayan Hari

Numerade Educator

Problem 68

Diffraction effects become significant when the width of an aperture is comparable to the wavelength of the waves being diffracted. (a) At what speed will the de Broglie wavelength of a $65-\mathrm{kg}$ student be equal to the $0.76-\mathrm{m}$ width of a doorway? (b) $\mathrm{At}$ this speed, how long will it take the student to travel a distance of $1.0 \mathrm{mm}$ ? (For comparison, the age of the universe is approximately $4 \times 10^{17}$ s.)

Narayan Hari

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Problem 69

A particle has a mass $m$ and an electric charge $q$. The particle is accelerated from rest through a potential difference $V$. What is the particle's de Broglie wavelength, expressed in terms of $m, q,$ and $V ?$

Nishant Kumar

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Problem 70

A baseball $(0.15 \mathrm{kg})$ and an electron both have a speed of $41 \mathrm{m} / \mathrm{s} .$ Find the uncertainty in position of each of these objects, given that the uncertainty in their speed is $5.0 \%$.

Narayan Hari

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Problem 71

The uncertainty in position of a proton confined to the nucleus of an atom is roughly the diameter of the nucleus. If this diameter is $7.5 \times 10^{-15} \mathrm{m},$ what is the uncertainty in the proton's momentum?

Narayan Hari

Numerade Educator

Problem 72

The position of a $0.26-\mathrm{kg}$ air-track cart is determined to within an uncertainty of $2.2 \mathrm{mm}$. What speed must the cart acquire as a result of the position measurement?

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Problem 73

The measurement of an electron's energy requires a time interval of $1.0 \times 10^{-8} \mathrm{s} .$ What is the smallest possible uncertainty in the electron's energy?

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Problem 74

Aparticle's energy is measured with an uncertainty of $0.0010 \mathrm{eV}$. What is the smallest possible uncertainty in our knowledge of when the particle had this energy?

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Problem 75

An excited state of a particular atom has a mean lifetime of $0.60 \times 10^{-9} \mathrm{s},$ which we may take as the uncertainty $\Delta t .$ What is the minimum uncertainty in any measurement of the energy of this state?

Zulfiqar Ali

Numerade Educator

Problem 76

The $\Sigma^{+}$ is an unstable particle, with a mean lifetime of $2.5 \times 10^{-10} \mathrm{s} .$ Its lifetime defines the uncertainty $\Delta t$ for this particle. What is the minimum uncertainty in this particle's energy?

Narayan Hari

Numerade Educator

Problem 77

The uncertainty in an electron's position is $0.15 \mathrm{nm}$. (a) What is the minimum uncertainty $\Delta p$ in its momentum? (b) What is the kinetic energy of an electron whose momentum is equal to this uncertainty $(\Delta p=p) ?$

Narayan Hari

Numerade Educator

Problem 78

The uncertainty in a proton's position is $0.15 \mathrm{nm}$. (a) What is the minimum uncertainty $\Delta p$ in its momentum? (b) What is the kinetic energy of a proton whose momentum is equal to this uncertainty $(\Delta p=p) ?$

Narayan Hari

Numerade Educator

Problem 79

An electron has a momentum $p$ s $1.7 \times 10^{-25} \mathrm{kg} \cdot \mathrm{m} / \mathrm{s}$ What is the minimum uncertainty in its position that will keep the relative uncertainty in its momentum $(\Delta p / p)$ below $1.0 \% ?$

Zulfiqar Ali

Numerade Educator

Problem 80

Suppose you perform an experiment on the photoelectric effect using light with a frequency high enough to eject electrons. If the intensity of the light is increased while the frequency is held constant, describe whether the following quantities increase, decrease, or stay the same:
(a) The maximum kinetic energy of an ejected electron;
(b) the minimum de Broglie wavelength of an electron; (c) the number of electrons ejected per second; (d) the electric current in the phototube.

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 81

Suppose you perform an experiment on the photoelectric effect using light with a frequency high enough to eject electrons. If the frequency of the light is increased while the intensity is held constant, describe whether the following quantities increase, decrease, or stay the same:
(a) The maximum kinetic energy of an ejected electron; (b) the minimum de Broglie wavelength of an electron;
(c) the number of electrons ejected per second; (d) the electric current in the phototube.

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 82

An electron that is accelerated from rest through a potential difference $V_{0}$ has a de Broglie wavelength $\lambda_{0}$. What potential difference will double the electron's wavelength? (Express your answer in terms of $V_{0-}$ )

Narayan Hari

Numerade Educator

Problem 83

A beam of particles diffracts from a crystal, producing an interference maximum at the angle $\theta$. (a) If the mass of the particles is increased, with everything else remaining the same, does the angle of the interference maximum increase, decrease, or stay the same? Explain (b). If the energy of the particles is increased, with everything else remaining the same, does the angle of the interference maximum increase, decrease, or stay the same? Explain.

Narayan Hari

Numerade Educator

Problem 84

You want to construct a photocell that works with visible light. Three materials are readily available: aluminum $\left(W_{0}=4.28 \mathrm{eV}\right)$ lead $\left(W_{0}=4.25 \mathrm{eV}\right),$ and cesium $\left(\mathrm{W}_{0}=2.14 \mathrm{eV}\right) .$ Which material(s) would be suitable?

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 85

Human Vision Studies have shown that some people can detect 545 -nm light with as few as 100 photons entering the eye per second. What is the power delivered by such a beam of light?

Narayan Hari

Numerade Educator

Problem 86

A pendulum consisting of a $0.15-k g$ mass attached to a $0.78-m$ string undergoes simple harmonic motion. (a) What is the frequency of oscillation for this pendulum? (b) Assuming the energy of this system satisfies $E_{n}=n h f,$ find the maximum speed of the $0.15-\mathrm{kg}$ mass when the quantum number is $1.0 \times 10^{33}$

Narayan Hari

Numerade Educator

Problem 87

To listen to a radio station, a certain home receiver must pick up a signal of at least $1.0 \times 10^{-10}$ W. (a) If the radio waves have a frequency of $96 \mathrm{MHz}$, how many photons must the receiver absorb per second to get the station? (b) How much force is exerted on the receiving antenna for the case considered in part (a)?

Narayan Hari

Numerade Educator

Problem 88

The latent heat for converting ice at $0^{\circ} \mathrm{C}$ to water at $0^{\circ} \mathrm{C}$ is $80.0 \mathrm{kcal} / \mathrm{kg}$ (Chapter 17$)$ (a) How many photons of frequency $6.0 \times 10^{14} \mathrm{Hz}$ must be absorbed by a $1.0-\mathrm{kg}$ block of ice at $0^{\circ} \mathrm{C}$ to melt it to water at $0^{\circ} \mathrm{C} ?$ (b) How many molecules of $\mathrm{H}_{2} \mathrm{O}$ can one photon convert from ice to water?

Zulfiqar Ali

Numerade Educator

Problem 89

How many $550-\mathrm{nm}$ photons would have to be absorbed to raise the temperature of $1.0 \mathrm{g}$ of water by $1.0 \mathrm{C}^{\circ} ?$

Narayan Hari

Numerade Educator

Problem 90

A microwave oven can heat $205 \mathrm{mL}$ of water from $20.0^{\circ} \mathrm{C}$ to $90.0^{\circ} \mathrm{C}$ in $2.00 \mathrm{min.}$ If the wavelength of the microwaves is $\lambda=12.2 \mathrm{cm},$ how many photons were absorbed by the water? (Assume no loss of heat by the water.)

Narayan Hari

Numerade Educator

Problem 91

Light with a frequency of $2.11 \times 10^{15} \mathrm{Hz}$ ejects electrons from the surface of lead, which has a work function of $4.25 \mathrm{eV}$. What is the minimum de Broglie wavelength of the ejected electrons?

Narayan Hari

Numerade Educator

Problem 92

An electron moving with a speed of $2.7 \times 10^{6} \mathrm{m} / \mathrm{s}$ has the same momentum as a photon. Find (a) the de Broglie wavelength of the electron and (b) the wavelength of the photon.

Narayan Hari

Numerade Educator

Problem 93

The Cold Light of Fireflies Fireflies are often said to give off "cold light." Given that the peak in a firefly's radiation occurs at about $5.4 \times 10^{14} \mathrm{Hz},$ determine the temperature of a blackbody that would have the same peak frequency. From your result, would you say that firefly radiation is well approximated by blackbody radiation? Explain.

Narayan Hari

Numerade Educator

Problem 94

When light with a wavelength of 545 nm shines on a metal surface, electrons are ejected with speeds of $3.10 \times 10^{5} \mathrm{m} / \mathrm{s}$ or less. (a) Give a strategy that allows you to use the preceding information to calculate the work function and cutoff frequency for this surface. (b) Carry out your strategy and determine the work function and cutoff frequency.

Narayan Hari

Numerade Educator

Problem 95

A hydrogen atom absorbs a 486.2 -nm photon. A short time later, the same atom emits a photon with a wavelength of $97.23 \mathrm{nm}$ (a) Has the net energy of the atom increased or decreased? Explain. (b) Calculate the change in energy of the hydrogen atom.

Narayan Hari

Numerade Educator

Problem 96

When a beam of atoms emerges from an oven at the absolute temperature $T,$ the most probable de Broglie wavelength for a given atom is
$$
\lambda_{\operatorname{mp}}=\frac{h}{\sqrt{5 m k T}}
$$
In this expression, $m$ is the mass of an atom, and $k$ is Boltzmann's constant (Chapter 17 ). What is the most probable speed of a hydrogen atom emerging from an oven at $450 \mathrm{K}$ ?

Zulfiqar Ali

Numerade Educator

Problem 97

(a) Does the de Broglie wavelength of a particle increase or decrease as its kinetic energy increases? Explain.
(b) Show that the de Broglie wavelength of an electron in nanometers can be written as $\lambda=(1.23 \mathrm{nm}) / \sqrt{K},$ where $K$ is the kinetic energy of the electron in eV. Use classical expressions for momentum and kinetic energy.

Narayan Hari

Numerade Educator

Problem 98

A jar is filled with monatomic helium gas at a temperature of $25^{\circ} \mathrm{C}$. The pressure inside the jar is one atmosphere; that is, $101 \mathrm{kPa} .$ (a) Find the average de Broglie wavelength of the helium atoms. (b) Calculate the average separation between helium atoms in the jar. (Note: The fact that the spacing between atoms is much greater than the de Broglie wavelength means quantum effects are negligible, and the a toms can be treated as particles.)

Narayan Hari

Numerade Educator

Problem 99

The Compton Wavelength The Compton wrovlength, $\lambda_{C}$, of a particle of mass $m$ is defined as follows: $\lambda_{C}=h / m c$
(a) Calculate the Compton wavelength of a proton.
(b) Calculate the energy of a photon that has the same wavelength as found in part (a). (c) Show, in general, that a photon with a wavelength equal to the Compton wavelength of a particle has an energy that is equal to the rest energy of the particle.

Narayan Hari

Numerade Educator

Problem 100

Light of frequency $8.22 \times 10^{14} \mathrm{Hz}$ ejects electrons from surface A with a maximum kinetic energy that is $2.00 \times 10^{-19} \mathrm{J}$ greater than the maximum kinetic energy of electrons ejected from surface B. (a) If the frequency of the light is increased, does the difference in maximum kinetic energy observed from the two surfaces increase, decrease, or stay the same? Explain.
(b) Calculate the difference in work function for these two surfaces.

Narayan Hari

Numerade Educator

Problem 101

What is the work function, $W_{0}$, for lithium, as determined from Millikan's results?
A. $0.0112 \mathrm{eV}$
B. $0.951 \mathrm{eV}$
C. $1.63 \mathrm{eV}$
D. $2.29 \mathrm{eV}$

Narayan Hari

Numerade Educator

Problem 102

What value does Millikan obtain for Planck's constant, based on the lithium measurements? (His value is close to, but not the same as, the currently accepted value.)
A. $1.12 \times 10^{-34} \mathrm{J} \cdot \mathrm{s}$
B. $3.84 \times 10^{-34} \mathrm{J} \cdot \mathrm{s}$
C. $6.14 \times 10^{-34} \mathrm{J} \cdot \mathrm{s}$
D. $6.57 \times 10^{-34} \mathrm{J} \cdot \mathrm{s}$

Narayan Hari

Numerade Educator

Problem 103

What maximum kinetic energy do you predict Millikan found when he used light with a wavelength of $365.0 \mathrm{nm} ?$
A. $0.805 \mathrm{eV}$
B. 1.08 eV
$\mathrm{C} \cdot 2.29 \mathrm{eV}$
D. $2.82 \mathrm{eV}$

Narayan Hari

Numerade Educator

Problem 104

Referring to Example $30-4$ An $X$ -ray photon with $\lambda=0.6500 \mathrm{nm}$ scatters from an electron, giving the electron a kinetic energy of $7.750 \mathrm{eV}$. (a) Is the scattering angle of the photon greater than, less than, or equal to $152^{\circ} ?$
(b) Find the scattering angle.

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator

Problem 105

Referring to Example $30-4$ An $\mathrm{X}$ -ray photon with $\lambda=0.6500 \mathrm{nm}$ scatters from an electron. The wavelength of the scattered photon is $0.6510 \mathrm{nm} .$ (a) Is the scattering angle in this case greater than, less than, or equal to $152^{\circ} ?$ (b) Find the scattering angle.

Khoobchandra Agrawal

Khoobchandra Agrawal

Numerade Educator