College Physics

Hugh D. Young

Chapter 28

Photons, Electrons, and Atoms - all with Video Answers

Educators

Chapter Questions

Problem 1

Response of the eye. The human eye is most sensitive to green light of wavelength 505 nm. Experiments have found that when people are kept in a dark room until their eyes adapt to the darkness, a single photon of green light will trigger receptor cells in the rods of the retina. (a) What is the frequency of this photon? (b) How much energy (in joules and eV) does it deliver what a small amount of energy this, is, calculate how fast a typical bacterium of mass $9.5 \times 10^{-12}$ g would move if it had that much energy.

Katie Mcalpine

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Problem 2

$\cdot$ An excited nucleus emits a gamma-ray photon with an energy of 2.45 MeV. (a) What is the photon's frequency? (b) What is the photon's wavelength? (c) How does this wave-length compare with a typical nuclear diameter of $10^{-14} \mathrm{m} ?$

Elan Stopnitzky

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Problem 3

A laser used to weld detached retinas emits light with a wavelength of 652 $\mathrm{nm}$ in pulses that are 20.0 $\mathrm{ms}$ in duration. The average power expended during each pulse is 0.600 $\mathrm{W}$ . (a) How much energy is in each pulse, in joules? In electron volts? (b) What is the energy of one photon in joules? In electron volts? (c) How many photons are in each pulse?

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Problem 4

A radio station broadcasts at a frequency of 92.0 $\mathrm{MHz}$ with a power output of 50.0 $\mathrm{kW}$ . (a) What is the energy of each emitted photon, in joules and electron volts? (b) How many photons are emitted per second?

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Problem 5

$\bullet$ The predominant wavelength emitted by an ultraviolet lamp is 248 nm. If the total power emitted at this wavelength is $12.0 \mathrm{W},$ how many photons are emitted per second?

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Problem 6

A photon has momentum of magnitude $8.24 \times 10^{-28} \mathrm{kg} \cdot \mathrm{m} / \mathrm{s}$ . (a) What is the energy of this photon? Give your answer in joules and in electron volts. (b) What is the wavelength of this photon? In what region of the electromagnetic spectrum does it lie?

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Problem 7

$\bullet$ In the photoelectric effect, what is the relationship between the threshold frequency $f_{0}$ and the work function $\phi ?$

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Problem 8

$\cdot$ A clean nickel surface is exposed to light of wavelength 235 $\mathrm{nm} .$ What is the maximum speed of the photoelectrons emitted from this surface? Use Table $28.1 .$

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Problem 9

$\bullet$ The photoelectric threshold wavelength of a tungsten surface is 272 $\mathrm{nm}$ . (a) What are the threshold frequency and work function (in eV) of this tungsten? (b) Calculate the maximum kinetic energy (in eV) of the electrons ejected from this tungsten surface by ultraviolet radiation of frequency $1.45 \times 10^{15} \mathrm{Hz}$

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Problem 10

$\bullet$ What would the minimum work function for a metal have to be for visible light (having wavelengths between 400 $\mathrm{nm}$ and 700 $\mathrm{nm} )$ to eject photoelectrons?

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Problem 11

. When ultraviolet light with a wavelength of 400.0 nm falls on a certain metal surface, the maximum kinetic energy of the emitted photoelectrons is measured to be 1.10 eV. What is the maximum kinetic energy of the photoelectrons when light of wavelength 300.0 nm falls on the same surface?

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Problem 12

When ultraviolet light with a wavelength of 254 nm falls upon a clean metal surface, the stopping potential necessary to terminate the emission of photoelectrons is 0.181 $\mathrm{V}$ . (a) What is the photoelectric threshold wavelength for this metal? (b) What is the work function for the metal?

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Problem 13

$\bullet$ The photoelectric work function of potassium is 2.3 $\mathrm{eV}$ . If light having a wavelength of 250 $\mathrm{nm}$ falls on potassium, find (a) the stopping potential in volts; (b) the kinetic energy, in electron volts, of the most energetic electrons ejected; (c) the speeds of these electrons.

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Problem 14

In a photoelectric effect experiment it is found that no cur- rent flows unless the incident light has a wavelength shorter than 289 $\mathrm{nm}$ (a) What is the work function of the metal sur- face? (b) What stopping potential will be needed to halt the current if light of 225 nm falls on the surface?

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Problem 15

.. Light with a wavelength range of $145-295$ nm shines on a silicon surface in a photoelectric effect apparatus, and a reversing potential of 3.50 $\mathrm{V}$ is applied to the resulting photoelectrons. (a) What is the longest wavelength of the light that will eject electrons from the silicon surface? (b) With what maximum kinetic energy will electrons reach the anode?

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Problem 16

$\bullet$ (a) How much energy is needed to ionize a hydrogen atom that is in the $n=4$ state? (b) What would be the wavelength of a photon emitted by a hydrogen atom in a transition from the $n=4$ state to the $n=2$ state?

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Problem 17

$\bullet$ Use Balmer's formula to calculate (a) the wavelength, (b) the frequency, and (c) the photon energy for the $\mathrm{H}_{\gamma}$ line of the Balmer series for hydrogen.

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Problem 18

$\cdot$ Find the longest and shortest wavelengths in the Lyman and Paschen series for hydrogen. In what region of the electromagnetic spectrum does each series lie?

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Problem 19

(a) Calculate the longest and shortest wavelengths for light in the Balmer, Lyman, and Brackett series. (b) Use your results from part (a) to decide in which part of the electromagnetic spectrum each of these series lies.

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Problem 20

$\bullet$ The energy-level scheme for the hypothetical one-electron element searsium is shown in Fig. $28.24 .$ The potential energy is taken to be zero for an electron at an infinite distance from the nucleus. (a) How much energy (in electron volts) does it take to ionize an electron from the ground level? (b) An 18 eV photon is absorbed by a searsium atom in its ground level. As the atom returns to its ground level, what possible energies can the emitted photons have? Assume that there can be transitions between all pairs of levels. (c) What will happen if a photon with an energy of 8 $\mathrm{eV}$ strikes a searsium atom in its ground level? Why? (d) Photons emitted in the searsium transitions $n=3 \rightarrow n=2$ and $n=3 \rightarrow n=1$ will eject photoelectrons from an unknown metal, but the photon emitted from the transition $n=4 \rightarrow n=3$ will not. What are the limits (maximum and minimum possible values) of the work function of the metal?

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Problem 21

$\bullet$ In a set of experiments on a hypothetical one-electron atom, you measure the wavelengths of the photons emitted from transitions ending in the ground state $(n=1),$ as shown in the energy-level diagram in Fig. $28.25 .$ You also observe that it takes 17.50 eV to ionize this atom. (a) What is the energy of the atom in each of the levels $(n=1, n=2,$ etc. $)$ shown in the figure? (b) If an electron made a transition from the $n=4$ to the $n=2$ level, what wavelength of light would it emit?

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Problem 22

$\cdot$ For a hydrogen atom in the ground state, determine, in electron volts, (a) the kinetic energy of the electron, (b) the potential energy, (c) the total energy, (d) the minimum energy required to remove the electron completely from the atom. (e) What wavelength does a photon with the energy calculated in part (d) have? In what region of the electromagnetic spectrum does it lie?

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Problem 23

$\bullet$ Use the Bohr model for the following calculations: (a) What is the speed of the electron in a hydrogen atom in the $n=1,2$ and 3 levels? (b) Calculate the radii of each of these levels. (c) Find the total energy (in eV) of the atom in each of these levels.

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Problem 24

. An electron in an excited state of hydrogen makes a transition from the $n=5$ level to the $n=2$ level. (a) Does the atom emit or absorb a photon during this process? How do you know? (b) Calculate the wavelength of the photon involved in the transition.

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Problem 25

$\bullet$ A hydrogen atom initially in the ground state absorbs a photon, which excites it to the $n=4$ state. Determine the wavelength and frequency of the photon.

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Problem 26

Light of wavelength 59 nm ionizes a hydrogen atom that was originally in its ground state. What is the kinetic energy of the ejected electron?

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Problem 27

\bullet A triply ionized beryllium ion, $\mathrm{Be}^{3+}$ (a beryllium atom with three electrons removed), behaves very much like a hydrogen atom, except that the nuclear charge is four times as great. (a) What is the ground-level energy of $\mathrm{Be}^{3+} ?$ How does this compare with the ground-level energy of the hydrogen atom? (b) What is the ionization energy of Be $^{3+} ?$ How does this compare with the ionization energy of the hydrogen atom? (c) For the hydrogen atom, the wavelength of the photon emitted in the transition $n=2$ to $n=1$ is 122 nm. (See Example 28.6 . What is the wavelength of the photon emitted when a $\mathrm{Be}^{3+}$ ion undergoes this transition? (d) For a given value of $n,$ how does the radius of an orbit in $\mathrm{Be}^{3+}$ compare with that for hydrogen?

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Problem 28

$\bullet$ (a) Use the information for neon shown in Fig. 28.26 to compute the energy difference for the $5 s-$ to- 3$p$ transition in neon. Express your result in electron volts and in joules. (b) Calculate the wavelength of a photon having this energy, and compare your result with the observed wavelength of the laser light. (c) What is the wavelength of the light from the $3 p-$ to- $-3 s$ transition in neon?

Elan Stopnitzky

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Problem 29

$\bullet$ The diode laser keychain you use to entertain your cat has a wavelength of 645 $\mathrm{nm}$ . If the laser emits $4.50 \times 10^{17}$ photons during a 30.0 s feline play session, what is its average power output?

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Problem 30

$\cdot$ Laser surgery. Using a mixture of $\mathrm{CO}_{2}, \mathrm{N}_{2},$ and sometimes
$\mathrm{He}, \mathrm{CO}_{2}$ lasers emit a wavelength of 10.6$\mu \mathrm{m} .$ At power outputs of $0.100 \mathrm{kW},$ such lasers are used for surgery. How many photons per second does a CO $_{2}$ laser deliver to the tissue during its use in an operation?

Elan Stopnitzky

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Problem 31

Photorefractive keratectomy (PRK) is a laser-based surgery process that corrects near- and farsightedness by removing part of the lens of the eye to change its curvature and hence focal length. This procedure can remove layers $0.25 \mu \mathrm{m}$ thick in pulses lasting $12.0 \mathrm{~ns}$ with a laser beam of wavelength $193 \mathrm{nm}$. Low-intensity beams can be used because each individual photon has enough energy to break the covalent bonds of the tissue. (a) In what part of the electromagnetic spectrum does this light lie? (b) What is the energy of a single photon? (c) If a $1.50 \mathrm{~mW}$ beam is used, how many photons are delivered to the lens in each pulse?

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Problem 32

$\cdot$ Removing birthmarks. Pulsed dye lasers emit light of wavelength 585 $\mathrm{nm}$ in 0.45 $\mathrm{ms}$ pulses to remove skin blemishes such as birthmarks. The beam is usually focused onto a circular spot 5.0 $\mathrm{mm}$ in diameter. Suppose that the output of one such laser is 20.0 $\mathrm{W}$ . (a) What is the energy of each photon, in eV? (b) How many photons per square millimeter are delivered to the blemish during each pulse?

Elan Stopnitzky

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Problem 33

$\bullet$ (a) What is the minimum potential difference between the filament and the target of an x-ray tube if the tube is to accelerate electrons to produce rays with a wavelength of 0.150 nm? (b) What is the shortest wavelength produced in an x-ray tube operated at 30.0 $\mathrm{kV}$ ? (c) Would the answers to parts (a) and (b) be different if the tube accelerated protons instead of electrons? Why or why not?

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Problem 34

$\cdot$ The cathode-ray tubes that generated the picture in early color televisions were sources of $x$ rays. If the acceleration voltage in a television tube is 15.0 $\mathrm{kV}$ , what are the shortest- wavelength $\mathrm{x}$ rays produced by the television? (Modern televisions contain shielding to stop these x rays.)

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Problem 35

$\cdot$ An x ray with a wavelength of 0.100 nm collides with a electron that is initially at rest. The $x$ ray's final wavelength 0.110 nm. What is the final kinetic energy of the electron?

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Problem 36

If a photon of wavelength 0.04250 nm strikes a free electron and is scattered at an angle of $35.0^{\circ}$ from its original direction, find (a) the change in the wavelength of this photon, (b) the wavelength of the scattered light, (c) the change in energy of the photon (is it a loss or a gain?), and (d) the energy gained by the electron.

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Problem 37

X rays with initial wavelength 0.0665 $\mathrm{nm}$ undergo Compton scattering. What is the longest wavelength found in the scattered $x$ rays? At which scattering angle is this wavelength observed?

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Problem 38

An incident $x$ -ray photon is scattered from a free electron that is initially at rest. The photon is scattered straight back at an angle of $180^{\circ}$ from its initial direction. The wavelength of the scattered photon is 0.0830 $\mathrm{nm.}$ (a) What is the wavelength of the incident photon? (b) What is the magnitude of the momentum of the electron after the collision? (c) What is the kinetic energy of the electron after the collision?

Elan Stopnitzky

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Problem 39

$\bullet$ Protons are accelerated from rest by a potential difference of 4.00 $\mathrm{kV}$ and strike a metal target. If a proton produces one photon on impact, what is the minimum wavelength of the resulting $\mathrm{x}$ rays? How does your answer compare to the minimum wavelength if 4.00 $\mathrm{keV}$ electrons are used instead? Why do x-ray tubes use electrons rather than protons
to produce $x$ rays?

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Problem 40

$\bullet$ (a) An electron moves with a speed of $4.70 \times 10^{6} \mathrm{m} / \mathrm{s}$ . What is its de Broglie wavelength? (b) A proton moves with the same speed. Determine its de Broglie wavelength.

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Problem 41

$\cdot$ How fast would an electron have to move so that its de Broglie wavelength would be 1.00 $\mathrm{mm}$ ?

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Problem 42

$\bullet$ (a) Approximately what range of photon energies (in eV) corresponds to the visible spectrum? (b) Approximately what range of wavelengths and kinetic energies would electrons in this energy range have?

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Problem 43

$\bullet$ In the Bohr model of the hydrogen atom, what is the de Broglie wavelength for the electron when it is in (a) the $n=1$ level and (b) the $n=4$ level? In each case, compare the de Broglie wavelength to the circumference 2$\pi r_{n}$ of the orbit.

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Problem 44

$\bullet$ (a) What is the de Broglie wavelength of an electron accelerated through 800 $\mathrm{V} ?$ (b) What is the de Broglie wavelength of a proton accelerated through the same potential difference?

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Problem 45

$\bullet$ Find the wavelengths of a photon and an electron that have the same energy of 25 $\mathrm{eV}$ . (The energy of the electron is its kinetic energy.)

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Problem 46

$\bullet$ (a) The uncertainty in the $x$ component of the position of a proton is $2.0 \times 10^{-12} \mathrm{m}$ . What is the minimum uncertainty in the $x$ component of the velocity of the proton? (b) The uncertainty in the $x$ component of the velocity of an electron is 0.250 $\mathrm{m} / \mathrm{s} .$ What is the minimum uncertainty in the $x$ coordinate of the electron?

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Problem 47

$\bullet$ A certain atom has an energy level 3.50 eV above the ground state. When excited to this state, it remains $4.0 \mu s,$ on the average, before emitting a photon and returning to the ground state. (a) What is the energy of the photon? What is its wavelength? (b) What is the smallest possible uncertainty in energy of the photon?

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Problem 48

A pesky 1.5 mg mosquito is annoying you as you attempt to study physics in your room, which is 5.0 $\mathrm{m}$ wide and 2.5 $\mathrm{m}$ high. You decide to swat the bothersome insect as it flies toward you, but you need to estimate its speed to make a successful hit. (a) What is the maximum uncertainty in the horizontal position of the mosquito? (b) What limit does the Heisenberg uncertainty principle place on your ability to know the horizontal velocity of this mosquito? Is this limitation a serious impediment to your attempt to swat it?

Elan Stopnitzky

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Problem 49

Suppose that the uncertainty in position of an electron is equal to the radius of the $n=1$ Bohr orbit, about $0.5 \times 10^{-10} \mathrm{m} .$ Calculate the minimum uncertainty in the cor- responding momentum the minimum uncertainty in the cor- magnitude of the momentum of the electron in the $n=1$ Bohr orbit.

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Problem 50

$\bullet$ (a) What accelerating potential is needed to produce electrons of wavelength 5.00 $\mathrm{nm}$ ? (b) What would be the energy of photons having the same wavelength as these electrons? (c) What would be the wavelength of photons having the same energy as the electrons in part (a)?

Elan Stopnitzky

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Problem 51

$\bullet$ (a) In an electron microscope, what accelerating voltage is needed to produce electrons with wavelength 0.0600 nm? (b) If protons are used instead of electrons, what accelerating voltage is needed to produce protons with wavelength 0.0600 nm? (Hint: In each case the initial kinetic energy is negligible.)

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Problem 52

Structure of a virus. To investigate the structure of extremely small objects, such as viruses, the wavelength of probing wave should be about one-tenth the size of the object for sharp images. But as the wavelength gets shorter, the energy of a photon of light gets greater and could damage or destroy the object being studied. One alternative is to use electron matter waves instead of light. Viruses vary considerably in size, but 50 $\mathrm{nm}$ is not unusual. Suppose you want to study such a virus, using a wave of wavelength 5.00 $\mathrm{nm}$ . (a) If you use light of this wavelength, what would be the energy (in eV) of a single photon? (b) If you use an electron of this wavelength, what would be its kinetic energy (in eV)? Is it now clear why matter waves (such as in the electron microscope) are often preferable to electromagnetic waves for studying microscopic objects?

Elan Stopnitzky

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Problem 53

$\bullet$ Exposing photographic film. The light-sensitive com- pound on most photographic films is silver bromide (AgBr). A film is "exposed" when the light energy absorbed dissociates this molecule into its atoms. (The actual process is more complex, but the quantitative result does not differ greatly.) The energy of dissociation of AgBr is $1.00 \times 10^{5} \mathrm{J} / \mathrm{mol}$ . For a photon that is just able to dissociate a molecule of silver bromide, find (a) the photon's energy in electron volts, (b) the wavelength of the photon, and (c) the frequency of the photon. (d) Light from a firefly can expose photographic film, but the radiation from an FM station broadcasting $50,000 \mathrm{W}$ at 100 $\mathrm{MHz}$ cannot. Explain why this is so, basing your answer on the energy of the photons involved.

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Problem 54

$\bullet$ A 2.50 $\mathrm{W}$ beam of light of wavelength 124 $\mathrm{nm}$ falls on a metal surface. You observe that the maximum kinetic energy of the ejected electrons is 4.16 $\mathrm{eV} .$ Assume that each photon in the beam ejects an electron. (a) What is the work function (in electron volts) of this metal? (b) How many photoelectrons are ejected each second from this metal? (c) If the power of the light beam, but not its wavelength, were reduced by half, what would be the answer to part (b)? (d) If the wavelength of the beam, but not its power, were reduced by half, what would be the answer to part (b)?

Elan Stopnitzky

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Problem 55

A sample of hydrogen atoms is irradiated with light with a wavelength of $85.5 \mathrm{nm},$ and electrons are observed leaving the gas. If each hydrogen atom were initially in its ground level, what would be the maximum kinetic energy, in electron volts, of these photoelectrons?

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Problem 56

An unknown element has a spectrum for absorption from its ground level with lines at $2.0,5.0,$ and 9.0 eV. Its ionization energy is 10.0 eV. (a) Draw an energy-level diagram for this element. (b) If a 9.0 eV photon is absorbed, what energies can the subsequently emitted photons have?

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Problem 57

(a) What is the least amount of energy, in electron volts, that must be given to a hydrogen atom which is initially in its ground level so that it can emit the $\mathrm{H}_{\alpha}$ line in the Balmer series? (b) How many different possibilities of spectral-line emissions are there for this atom when the electron starts in the $n=3$ level and eventually ends up in the ground level? Calculate the wavelength of the emitted photon in each case.

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Problem 58

$\bullet$ A specimen of the microorganism Gastropus hyptopus measures 0.0020 $\mathrm{cm}$ in length and can swim at a speed of 2.9 times its body length per second. The tiny animal has a mass of roughly $8.0 \times 10^{-12} \mathrm{kg}$ . (a) Calculate the de Broglie wave- length of this organism when it is swimming at top speed. (b) Calculate the kinetic energy of the organism (in eV) when it is swimming at top speed.

Elan Stopnitzky

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Problem 59

$\bullet$ A photon with a wavelength of 0.1800 nm is Compton scattered through an angle of $180^{\circ} .$ (a) What is the wavelength of the scattered photon? (b) How much energy is given to the electron? (c) What is the recoil speed of the electron? Is it necessary to use the relativistic kinetic-energy relationship?

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Problem 60

$\bullet$ (a) Calculate the maximum increase in photon wavelength that can occur during Compton scattering. (b) What is the energy (in electron volts) of the smallest-energy x-ray photon for which Compton scattering could result in doubling the original wavelength?

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Problem 61

An incident $x$ -ray photon of wavelength 0.0900 nm is scattered in the backward direction from a free electron that is initially at rest. (a) What is the magnitude of the momentum of the scattered photon? (b) What is the kinetic energy of the electron after the photon is scattered?

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Problem 62

A photon with wavelength of 0.1100 nm collides with a free electron that is initially at rest. After the collision, the photon's wavelength is 0.132 $\mathrm{nm}$ . (a) What is the kinetic energy of the electron after the collision? What is its speed? (b) If the electron is suddenly stopped (for example, in a solid target), all of its kinetic energy is used to create a photon. What is the wavelength of this photon?

Elan Stopnitzky

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Problem 63

From the kinetic-molecular theory of an ideal gas (Chapter 15$)$ we know that the average kinetic energy of an atom is $\frac{3}{2} k T$ . What is the wavelength of a photon that has this energy for a temperature of $27^{\circ} \mathrm{C} ?$

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Problem 64

Doorway diffraction. If your wavelength were $1.0 \mathrm{m},$ you would undergo considerable diffraction in moving through a doorway. (a) What must your speed be for you to have this wavelength? (Assume that your mass is 60.0 $\mathrm{kg} .$ ) (b) At the speed calculated in part (a), how many years would it take you to move 0.80 $\mathrm{m}$ (one step)? Will you notice diffraction effects
as you walk through doorways?

Elan Stopnitzky

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Problem 65

$\cdot$ What is the de Broglie wavelength of a red blood cell with a mass of $1.00 \times 10^{-11} \mathrm{g}$ that is moving with a speed of 0.400 $\mathrm{cm} / \mathrm{s} ?$ Do we need to be concerned with the wave nature of the blood cells when we describe the flow of blood in the body?

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Problem 66

$\bullet$ Removing vascular lesions. A pulsed dye laser emits light of wavelength 585 nm in 450$\mu$ s pulses. Because this wave- length is strongly absorbed by the hemoglobin in the blood, the method is especially effective for removing various types of blemishes due to blood, such as port-wine-colored birth-marks. To get a reasonable estimate of the power required for such laser surgery, we can model the blood as having the same specific heat and heat of vaporization as water $(4190 \mathrm{J} / \mathrm{kg} \cdot \mathrm{K}$ , $2.256 \times 10^{6} \mathrm{J} / \mathrm{kg} ) .$ Suppose that each pulse must remove 2.0$\mu g$ of blood by evaporating it, starting at $33^{\circ} \mathrm{C}$ . (a) How
much energy must each pulse deliver to the blemish? (b) What must be the power output of this laser? (c) How many photons does each pulse deliver to the blemish?

Elan Stopnitzky

Elan Stopnitzky

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Problem 67

$\bullet($ a) What is the energy of a photon that has wavelength 0.10$\mu m ?$ (b) Through approximately what potential difference must electrons be accelerated so that they will exhibit wave nature in passing through a pinhole 0.10$\mu m$ in diameter? What is the speed of these electrons? (c) If protons rather than electrons were used, through what potential difference would protons have to be accelerated so they would exhibit wave nature in passing through this pinhole? What would be the speed of these protons?

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Problem 68

$\bullet$ In a parallel universe, the value of Planck's constant is 0.0663 $\mathrm{J} \cdot$ s. Assume that the physical laws and all other physical constants are the same as in our universe. In this other universe, two physics students are playing catch with a baseball. They are 50 $\mathrm{m}$ apart, and one throws a 0.10 $\mathrm{kg}$ ball with a speed of 5.0 $\mathrm{m} / \mathrm{s}$ (a) What is the uncertainty in the ball's horizontal momentum in a direction perpendicular to that in which it is being thrown if the student throwing the ball knows that is located within a cube with volume 1000 $\mathrm{cm}^{3}$ at the time she throws it? (b) By what horizontal distance could the ball miss
the second student?

Elan Stopnitzky

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Problem 69

$\bullet$ The neutral $\pi^{\circ}$ meson is an unstable particle produced in high-energy particle collisions. Its mass is about 264 times that of the electron, and it exists for an average lifetime of $8.4 \times 10^{-17}$ s before decaying into two gamma-ray photons. Assuming that the mass and energy of the particle are related by the Einstein relation $E=m c^{2},$ find the uncertainty in the mass of the particle and express it as a fraction of the particle's mass.

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Problem 70

$\bullet$ A beam of electrons is accelerated from rest and then passes through a pair of identical thin slits that are 1.25 $\mathrm{nm}$ apart. You observe that the first double-slit interference dark fringe occurs at $\pm 18.0^{\circ}$ from the original direction of the beam when viewed on a distant screen. (a) Are these electrons relativistic? How do you know? (b) Through what potential difference were the electrons accelerated? focused on the tumor. The tissue absorbs the energy predominately via Compton interactions, so it is important to know how many Compton interactions occur and how many ionizations a single Compton electron produces. A linear accelerator used in radiation therapy produces x ray photons with an average energy of about 2 MeV, each of which impart 1 MeV to the Compton electrons. A typical tumor has $10^{8}$ cells/cm $^{3}$ and a full treatment may involve a dose of 70 Gy in 35 fractional exposures on different days. The gray (Gy) is a measure of the absorbed energy dose of radiation per unit mass of tissue, expressed in the units of $\mathrm{J} / \mathrm{kg}$ .

Elan Stopnitzky

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Numerade Educator

Problem 71

How much energy is imparted to a cell during one day's treatment? Assume that the specific gravity of the tumor is 1 and that $1 \mathrm{J}=6 \times 10^{18} \mathrm{eV}$
A. 12 $\mathrm{MeV} / \mathrm{cell}$
B. 120 $\mathrm{MeV} / \mathrm{cell}$
C. 120 $\mathrm{MeV} / \mathrm{cell}$
D. $120 \times 10^{3} \mathrm{MeV} / \mathrm{cell}$

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Problem 72

Suppose the answer to problem 71 is 12 MeV/cell. How many Compton interactions will occur per cell in a single day's treatment?
A. $120 \times 10^{6}$
B. $120 \times 10^{4}$
C. $120 \times 10^{2}$
D. 12

Elan Stopnitzky

Elan Stopnitzky

Numerade Educator

Problem 73

Each Compton electron causes a series of ionization in the tissue as it interacts with molecules (mainly water), and each ionization takes about 40 eV. How many ionizations occur in a single cell as a result of a day's treatment?
A. 3
B. $3 \times 10^{4}$
C. $3 \times 10^{4}$
D. $3 \times 10^{6}$

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