College Physics

lan Giambattista, Betty McCarthy Richardson, Robert C. Richardson

Chapter 27

Early Quantum Physics and the Photon - all with Video Answers

Educators

Chapter Questions

Problem 1

A 200-W infrared laser emits photons with a wavelength of $2.0 \times 10^{-6} \mathrm{~m}$ while a 200-W ultraviolet light emits photons with a wavelength of $7.0 \times 10^{-8} \mathrm{~m}$. (a) Which has greater energy, a single infrared photon or a single ultraviolet photon? (b) What is the energy of a single infrared photon and the energy of a single ultraviolet photon? (c) How many photons of each kind are emitted per second?

Guilherme Barros

Guilherme Barros

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Problem 2

What is the energy of a photon of light of wavelength $0.70 \mu \mathrm{m} ?$

Guilherme Barros

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Problem 3

Find the (a) wavelength and (b) frequency of a $3.1-\mathrm{eV}$ photon.

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Problem 4

The photoelectric threshold frequency of silver is $1.04$ $\times 10^{15} \mathrm{~Hz}$. What is the minimum energy required to remove an electron from silver?

Guilherme Barros

Guilherme Barros

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Problem 5

A rubidium surface has a work function of $2.16 \mathrm{eV}$. (a) What is the maximum kinetic energy of ejected electrons if the incident radiation is of wavelength $413 \mathrm{~nm}$ ? (b) What is the threshold wavelength for this surface?

Guilherme Barros

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Problem 6

A clean iron surface is illuminated by ultraviolet light. No photoelectrons are ejected until the wavelength of the incident UV light falls below $288 \mathrm{~nm}$. (a) What is the work function (in $\mathrm{eV}$ ) of the metal? (b) What is the maximum kinetic energy for electrons ejected by incident light of wavelength $140 \mathrm{~nm}$ ?

Brian Francisco

Brian Francisco

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Problem 7

The minimum energy required to remove an electron from a metal is $2.60 \mathrm{eV}$. What is the longest wavelength photon that can eject an electron from this metal?

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Problem 8

Photons of wavelength $350 \mathrm{~nm}$ are incident on a metal plate in a photocell and electrons are ejected. A stopping potential of $1.10 \mathrm{~V}$ is able to just prevent any of the ejected electrons from reaching the opposite electrode. What is the maximum wavelength of photons that will eject electrons from this metal?

Guilherme Barros

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Problem 9

Ultraviolet light of wavelength $220 \mathrm{~nm}$ illuminates a tungsten surface and electrons are ejected. A stopping potential of $1.1 \mathrm{~V}$ is able to just prevent any of the ejected electrons from reaching the opposite electrode. What is the work function for tungsten?

Guilherme Barros

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Problem 10

Photons with a wavelength of $400 \mathrm{~nm}$ are incident on an unknown metal and electrons are ejected from the metal. However, when photons with a wavelength of $700 \mathrm{~nm}$ are incident on the metal, no electrons are ejected. (a) Could this metal be cesium with a work function of $1.8 \mathrm{eV} ?$ (b) Could this metal be tungsten with a work function of $4.6 \mathrm{eV} ?$ (c) Calculate the maximum kinetic energy of the ejected electrons for each possible metal when $200-\mathrm{nm}$ photons are incident on it.

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Problem 11

Two different monochromatic light sources, one yellow $(580 \mathrm{~nm})$ and one violet $(425 \mathrm{~nm})$, are used in a photoelectric effect experiment. The metal surface has a photoelectric threshold frequency of $6.20 \times 10^{14} \mathrm{~Hz}$
(a) Are both sources able to eject photoelectrons from the metal? Explain. (b) How much energy is required to eject an electron from the metal? (Use $h=4.136 \times$ $\left.10^{-15} \mathrm{eV} \cdot \mathrm{s} .\right)$

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Problem 12

(a) Light of wavelength $300 \mathrm{~nm}$ is incident upon a metal that has a work function of $1.4 \mathrm{eV}$. What is the maximum speed of the emitted electrons? (b) Repeat part (a) for light of wavelength $800 \mathrm{~nm}$ incident upon a metal that has a work function of $1.6 \mathrm{eV}$. (c) How would your answers to parts (a) and (b) vary if the light intensity were doubled?

Brian Francisco

Brian Francisco

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Problem 13

Calculate the value of (a) Planck's constant and (b) the work function of the metal from the data obtained by Robert A. Millikan in 1916 . Millikan was attempting to disprove the Einstein photoelectric equation; instead he found that his data supported Einstein's prediction.

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Problem 14

A $640-\mathrm{nm}$ laser emits a one-second pulse in a beam with a diameter of $1.5 \mathrm{~mm}$. The rms electric field of the pulse is $120 \mathrm{~V} / \mathrm{m}$. How many photons are emitted per second?

Narayan Hari

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Problem 15

If the shortest wavelength produced by an $\mathrm{x}$ -ray tube is $0.46 \mathrm{~nm}$, what is the voltage applied to the tube?

Guilherme Barros

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Problem 16

What is the minimum potential difference applied to an xray tube if $x$ -rays of wavelength $0.250 \mathrm{~nm}$ are produced?

Devi Dutta Biswajeet

Devi Dutta Biswajeet

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Problem 17

What is the cutoff frequency for an $x$ -ray tube operating at $46 \mathrm{kV} ?$

Guilherme Barros

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Problem 18

The potential difference in an $\mathrm{x}$ -ray tube is $40.0 \mathrm{kV}$. What is the minimum wavelength of the continuous $\mathrm{x}$ ray spectrum emitted from the tube?

Guilherme Barros

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Problem 19

In a color TV tube, electrons are accelerated through a potential difference of $20.0 \mathrm{kV}$. Some of the electrons strike the metal mask (instead of the phosphor dots behind holes in the mask), causing $x$ -rays to be emitted. What is the smallest wavelength of the $\mathrm{x}$ -rays emitted?

Guilherme Barros

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Problem 20

Show that the cutoff frequency for an $x$ -ray tube is proportional to the potential difference through which the electrons are accelerated.

Guilherme Barros

Guilherme Barros

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Problem 21

A photon is incident on an electron at rest. The scattered photon has a wavelength of $2.81 \mathrm{pm}$ and moves at an angle of $29.5^{\circ}$ with respect to the direction of the incident photon. (a) What is the wavelength of the incident photon? (b) What is the final kinetic energy of the electron?

Guilherme Barros

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Problem 22

X-rays of wavelength $10.0 \mathrm{pm}$ are incident on a target. Find the wavelengths of the x-rays scattered at (a) $45.0^{\circ}$ and (b) $90.0^{\circ}$.

Narayan Hari

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Problem 23

An $\mathrm{x}$ -ray photon of wavelength $0.150 \mathrm{~nm}$ collides with an electron initially at rest. The scattered photon moves off at an angle of $80.0^{\circ}$ from the direction of the incident photon. Find (a) the Compton shift in wavelength and (b) the wavelength of the scattered photon.

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Problem 24

An incident beam of photons is scattered through $100.0^{\circ}$; the wavelength of the scattered photons is $124.65 \mathrm{pm}$. What is the wavelength of the incident photons?

Guilherme Barros

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Problem 25

An $\mathrm{x}$ -ray photon of initial frequency $3.0 \times 10^{19} \mathrm{~Hz}$ collides with a free electron at rest; the scattered photon moves off at $90^{\circ} .$ What is the frequency of the scattered photon?

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Guilherme Barros

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Problem 26

A photon of wavelength $0.14800 \mathrm{~nm}$, traveling due east, is scattered by an electron initially at rest. The wavelength of the scattered photon is $0.14900 \mathrm{~nm}$ and it moves at an angle $\theta$ north of east. (a) Find $\theta$. (b) What is the south component of the electron's momentum?

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Problem 27

What is the velocity of the scattered electron in Problem 26 ?

Dominador Tan

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Problem 28

A photon of energy $240.0 \mathrm{keV}$ is scattered by a free electron. If the recoil electron has a kinetic energy of $190.0 \mathrm{keV}$, what is the wavelength of the scattered photon?

Guilherme Barros

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Problem 29

An incident photon of wavelength $0.0100 \mathrm{~nm}$ is Compton scattered; the scattered photon has a wavelength of $0.0124 \mathrm{~nm}$. What is the change in kinetic energy of the electron that scattered the photon?

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Problem 30

A Compton scattering experiment is performed using an aluminum target. The incident photons have wavelength $\lambda$. The scattered photons have wavelengths $\lambda^{\prime}$ and energies $E$ that depend on the scattering angle $\theta$.
(a) At what angle $\theta$ are scattered photons with the smallest energy detected? (b) At this same scattering angle $\theta$, what is the ratio $\lambda^{\prime} / \lambda$ for $\lambda=10.0 \mathrm{pm}$ ?

Guilherme Barros

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Problem 31

What is the orbital radius of the electron in the $n=3$ state of hydrogen?

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Problem 32

Find the energy for a hydrogen atom in the stationary state $n=4$.

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Problem 33

(a) What is the difference in radius between the $n=1$ state and the $n=2$ state for hydrogen? (b) What is the difference in radius between the $n=100$ state and the $n=101$ state for hydrogen? How do the neighboring orbital separations compare for large and small $n$ values?

Guilherme Barros

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Problem 34

Find the Bohr radius of doubly ionized lithium $\left(\mathrm{Li}^{2+}\right)$.

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Guilherme Barros

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Problem 35

Find the energy in $\mathrm{eV}$ required to remove the remaining electron from a doubly ionized lithium $\left(\mathrm{Li}^{2+}\right)$ atom.

Devi Dutta Biswajeet

Devi Dutta Biswajeet

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Problem 36

How much energy must be supplied to a hydrogen atom to cause a transition from the ground state to the $n=4$ state?

Guilherme Barros

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Problem 37

A hydrogen atom in its ground state absorbs a photon of energy $12.1 \mathrm{eV}$. To what energy level is the atom excited?

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Problem 38

The Bohr theory of the hydrogen atom neglects gravitational forces between the electron and the proton. Make a calculation to justify this omission. [Hint: Find the ratio of the gravitational and electrostatic forces acting on the electron due to the proton.]

Brian Francisco

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Problem 39

Use the Bohr theory to find the energy necessary to remove the electron from a hydrogen atom initially in its ground state.

Guilherme Barros

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Problem 40

How much energy is required to ionize a hydrogen atom initially in the $n=2$ state?

Guilherme Barros

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Problem 41

What is the smallest energy photon that can be absorbed by a hydrogen atom in its ground state?

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Problem 42

Find the wavelength of the radiation emitted when a hydrogen atom makes a transition from the $n=6$ to the $n=3$ state.

Narayan Hari

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Problem 43

An electron orbits a proton at constant speed in a circle of radius $r$. (a) Using Coulomb's law, write an expression for the magnitude of the electric force on the electron in terms of $r$, the elementary charge $e$, and the Coulomb constant $k$. (b) Apply Newton's second law to the electron and use it to show that the electron's speed is
$$
v=\sqrt{\frac{k e^{2}}{m_{\mathrm{e}} r}}
$$
[Hint: The electron is in uniform circular motion.] (c) Use the Bohr assumption about the electron's angular momentum, Eq. ( $27-17$ ), to show that the radius of the $n$ th Bohr orbit is
$$
r_{n}=\frac{n^{2} \hbar^{2}}{m_{\mathrm{e}} k e^{2}}
$$

Katie Mcalpine

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Problem 44

An electron orbits a proton at constant speed in a circle of radius $r$. (a) What is the electron's kinetic energy in terms of $k, e$, and $r ?$ Use the expression for the electron's speed found in Problem 43 . (b) What is the electron's electric potential energy in terms of $k, e$, and $r ?$ (Assume $U=0$ when $r=\infty$.) (c) Show that the electron's mechanical energy $(K+U)$ is $E=-k e^{2} /(2 r) .$ (d) Use Eq. ( $27-19$ ) to show that the energy of the $n$ th Bohr orbit is
$$
E_{n}=-\frac{m_{\mathrm{e}} k^{2} e^{4}}{2 n^{2} \hbar^{2}}
$$

Katie Mcalpine

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Problem 45

By directly substituting the values of the fundamental constants, show that the Bohr radius $a_{0}=\hbar^{2} /\left(m_{\mathrm{e}} k e^{2}\right)$ has the numerical value $5.29 \times 10^{-11} \mathrm{~m}$.

Guilherme Barros

Guilherme Barros

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Problem 46

By directly substituting the values of the fundamental constants, show that the ground state energy for hydrogen in the Bohr model $E_{1}=-m_{\mathrm{e}} k^{2} e^{4} /\left(2 \hbar^{2}\right)$ has the numerical value $-13.6 \mathrm{eV}$.

Guilherme Barros

Guilherme Barros

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Problem 47

Calculate, according to the Bohr model, the speed of the electron in the ground state of the hydrogen atom.

Guilherme Barros

Guilherme Barros

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Problem 48

Find the speed of the electron in the ground state of He ${ }^{+}$

Devi Dutta Biswajeet

Devi Dutta Biswajeet

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Problem 49

One line in the helium spectrum is bright yellow and has the wavelength $587.6 \mathrm{~nm}$. What is the difference in energy (in eV) between two helium levels that produce this line?

Guilherme Barros

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Problem 50

A particle collides with a hydrogen atom in the $n=2$ state, transferring $15.0 \mathrm{eV}$ of energy to the atom. As a result, the electron breaks away from the hydrogen nucleus. What is the kinetic energy of the electron when it is far from the nucleus?

Guilherme Barros

Guilherme Barros

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Problem 51

A hydrogen atom has an electron in the $n=5$ level.
(a) If the electron returns to the ground state by emitting radiation, what is the minimum number of photons that can be emitted? (b) What is the maximum number that might be emitted?

Guilherme Barros

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Problem 52

The Paschen series in the hydrogen emission spectrum is formed by electron transitions from $n_{\mathrm{i}}>3$ to $n_{\mathrm{f}}=3$.
(a) What is the longest wavelength in the Paschen series? (b) What is the wavelength of the series limit (the lower bound of the wavelengths in the series)?
(c) In what part or parts of the EM spectrum is the Paschen series found (IR, visible, UV, etc.)?

Guilherme Barros

Guilherme Barros

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Problem 53

A fluorescent solid absorbs a photon of ultraviolet light of wavelength $320 \mathrm{~nm}$. If the solid dissipates $0.500 \mathrm{eV}$ of the energy and emits the rest in a single photon, what is the wavelength of the emitted light?

Guilherme Barros

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Problem 54

(a) Find the energies of the first four levels of doubly ionized lithium $\left(\mathrm{Li}^{2+}\right)$, starting with $n=1 .(\mathrm{b})$ What are the energies of the photons emitted or absorbed when the electron makes a transition between these levels?
(c) Are any of the photons in the visible part of the EM spectrum?

Guilherme Barros

Guilherme Barros

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Problem 55

A photon with a wavelength in the visible region (between 400 and $700 \mathrm{~nm}$ ) causes a transition from the $n$ to the $(n+1)$ state in doubly ionized lithium $\left(\mathrm{Li}^{2+}\right) .$ What is the lowest value of $n$ for which this could occur?

Guilherme Barros

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Problem 56

What is the maximum wavelength of a photon that can create an electron-positron pair?

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Guilherme Barros

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Problem 57

A detector shows evidence of the creation of an electron positron pair. If the tracks of the particles indicate that each one has a kinetic energy of $0.22 \mathrm{MeV}$, what is the energy of the photon that created the two particles?

Anand Jangid

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Problem 58

A photon passes near a nucleus and creates an electron and a positron, each with a total energy of $8.0 \mathrm{MeV}$. What was the wavelength of the photon?

Guilherme Barros

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Problem 59

A positron and an electron that were at rest suddenly vanish and two photons of identical frequency appear. What is the wavelength of each of these photons?

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Problem 60

A muon and an antimuon, each with a mass that is 207 times greater than an electron, were at rest when they annihilated and produced two photons of equal energy. What is the wavelength of each of the photons?

Guilherme Barros

Guilherme Barros

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Problem 61

In gamma-ray astronomy, the existence of positrons (e) can be inferred by a characteristic gamma ray that is emitted when a positron and an electron (e ) annihilate. For simplicity, assume that the electron and positron are at rest with respect to an Earth observer when they annihilate and that nothing else is in the vicinity. (a) Consider the reactions $\mathrm{e}^{-}+\mathrm{e}^{+} \rightarrow \gamma$, where the annihilation of the two particles at rest produces one photon, and $\mathrm{e}^{-}+\mathrm{e}^{+} \rightarrow 2 \gamma$, where the annihilation produces two photons. Explain why the first reaction does not occur, while the second does. (b) Suppose the reaction $\mathrm{e}^{-}+\mathrm{e}^{+} \rightarrow 2 \gamma$ occurs and one of the photons travels toward Earth. What is the energy of the photon?

Guilherme Barros

Guilherme Barros

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Problem 62

A surgeon is attempting to correct a detached retina by using a pulsed laser. (a) If the pulses last for $20.0 \mathrm{~ms}$ and if the output power of the laser is $0.500 \mathrm{~W}$, how much energy is in each pulse? (b) If the wavelength of the laser light is $643 \mathrm{~nm}$, how many photons are present in each pulse?

Guilherme Barros

Guilherme Barros

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Problem 63

These data are obtained for photoelectric stopping potentials using light of four different wavelengths.
(a) Plot a graph of the stopping potential versus the reciprocal of the wavelength. (b) Read the values of the work function and threshold wavelength for the metal used directly from the graph. (c) What is the slope of the graph? Compare the slope to the expected value (calculated from fundamental constants).

Dominador Tan

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Problem 64

An FM radio station broadcasts at a frequency of $89.3$ MHz. The power radiated from the antenna is $50.0 \mathrm{~kW}$. (a) What is the energy in eV of each photon radiated by the antenna? (b) How many photons per second does the antenna emit?

Guilherme Barros

Guilherme Barros

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Problem 65

An owl has good night vision because its eyes can detect a light intensity as small as $5.0 \times 10^{-13} \mathrm{~W} / \mathrm{m}^{2}$ What is the minimum number of photons per second that an owl eye can detect if its pupil has a diameter of $8.5 \mathrm{~mm}$ and the light has a wavelength of $510 \mathrm{~nm}$ ?

Vishal Gupta

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Problem 66

What is the shortest wavelength $x$ -ray produced by a $0.20$ -MV $x$ -ray machine?

Guilherme Barros

Guilherme Barros

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Problem 67

How much energy is required to remove an electron from a hydrogen atom in the $n=4$ state?

Guilherme Barros

Guilherme Barros

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Problem 68

During a Compton scattering experiment, an electron that was initially at rest recoils in the direction of motion of the incident $\mathrm{x}$ -ray photon. If the recoil electron has a kinetic energy of $0.20 \mathrm{keV}$, what is the wavelength of the incident $x$ -ray? What is the wavelength of the scattered $x$ -ray?

Guilherme Barros

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Problem 69

Compare the orbital radii of the $\mathrm{He}^{+}$ and $\mathrm{H}$ atoms for levels of equal energy (not the same value of $n$ ). Can you draw a general conclusion from your results?

Guilherme Barros

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Problem 70

According to the Bohr model, the speed of the electron in the ground state of singly ionized helium $\left(\mathrm{He}^{+}\right.$, with $Z=2$ ) is $4.4 \times 10^{6} \mathrm{~m} / \mathrm{s}$. Use this information to find the speed of an electron in the first excited state of triply ionized beryllium $\left(\mathrm{Be}^{3+}\right.$ with $Z=4$ ).

Guilherme Barros

Guilherme Barros

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Problem 71

The output power of a laser pointer is about $1 \mathrm{~mW}$.
(a) What are the energy and momentum of one laser photon if the laser wavelength is $670 \mathrm{~nm} ?$ (b) How many photons per second are emitted by the laser?
(c) What is the average force on the laser due to the momentum carried away by these photons?

Guilherme Barros

Guilherme Barros

Numerade Educator

Problem 72

In a photoelectric experiment using sodium, when incident light of wavelength $570 \mathrm{~nm}$ and intensity $1.0 \mathrm{~W} / \mathrm{m}^{2}$ is used, the measured stopping potential is $0.28 \mathrm{~V}$. (a) What would the stopping potential be for incident light of wavelength $400.0 \mathrm{~nm}$ and intensity 1.0 $\mathrm{W} / \mathrm{m}^{2} ?$ (b) What would the stopping potential be for incident light of wavelength $570 \mathrm{~nm}$ and intensity $2.0 \mathrm{~W} / \mathrm{m}^{2} ?(\mathrm{c})$ What is the work function of sodium?

Guilherme Barros

Guilherme Barros

Numerade Educator

Problem 73

A hydrogen atom in its ground state is immersed in a continuous spectrum of ultraviolet light with wavelengths ranging from $96 \mathrm{~nm}$ to $110 \mathrm{~nm}$. After absorbing a photon, the atom emits one or more photons to return to the ground state. (a) What wavelength(s) can be absorbed by the $\mathrm{H}$ atom? (b) For each of the possibilities in (a), if the atom is at rest before absorbing the UV photon, what is its recoil speed after absorption (but before emitting any photons)? (c) For each of the possibilities in (a), how many different ways are there for the atom to return to the ground state?

Guilherme Barros

Guilherme Barros

Numerade Educator

Problem 74

A 100-W lightbulb radiates visible light at a rate of about $10 \mathrm{~W} ;$ the rest of the $\mathrm{EM}$ radiation is mostly infrared. Assume that the lightbulb radiates uniformly in all directions. Under ideal conditions, the eye can see the lightbulb if at least 20 visible photons per second enter a dark-adapted eye with a pupil diameter of $7 \mathrm{~mm}$.
(a) Estimate how far from the source the lightbulb can be seen under these rather extreme conditions. Assume an average wavelength of $600 \mathrm{~nm}$. (b) Why do we not normally see lightbulbs at anywhere near this distance?

Guilherme Barros

Guilherme Barros

Numerade Educator

Problem 75

A thin aluminum target is illuminated with photons of wavelength $\lambda$. A detector is placed at $90.0^{\circ}$ to the direction of the incident photons. The scattered photons detected are found to have half the energy of the incident photons. (a) Find $\lambda$. (b) What is the wavelength of back scattered photons (detector at $\left.180^{\circ}\right) ?$ (c) What (if anything) would change if a copper target were used instead of an aluminum one?

Guilherme Barros

Guilherme Barros

Numerade Educator

Problem 76

What potential difference must be applied to an $x$ -ray tube to produce $x$ -rays with a minimum wavelength of $45.0 \mathrm{pm} ?$

Guilherme Barros

Guilherme Barros

Numerade Educator

Problem 77

What happens to the energies of the characteristic $\mathrm{x}-$ rays when the potential difference accelerating the electrons in an $\mathrm{x}$ -ray tube is doubled?

Guilherme Barros

Guilherme Barros

Numerade Educator

Problem 78

Nuclei in a radium- 226 radioactive source emit photons whose energy is $186 \mathrm{keV}$. These photons are scattered by the electrons in a metal target; a detector measures the energy of the scattered photons as a function of the angle $\theta$ through which they are scattered. Find the energy of the $\gamma$ -rays scattered through $\theta=90.0^{\circ}$ and $180.0^{\circ}$.

Guilherme Barros

Guilherme Barros

Numerade Educator

Problem 79

What is the ground state energy, according to Bohr theory, for (a) $\mathrm{He}^{+},(\mathrm{b}) \mathrm{Li}^{2+},(\mathrm{c})$ deuterium (an isotope of hydrogen whose nucleus contains a neutron as well as a proton)?

Guilherme Barros

Guilherme Barros

Numerade Educator

Problem 80

Follow the steps outlined in this problem to estimate the time lag (predicted classically but not observed experimentally) in the photoelectric effect. Let the intensity of the incident radiation be $0.01 \mathrm{~W} / \mathrm{m}^{2}$. (a) If the area of the atom is $(0.1 \mathrm{~nm})^{2}$, find the energy per second falling on the atom.
(b) If the work function is $2.0 \mathrm{eV}$, how long would it take (classically) for enough energy to fall on this area to liberate one photoelectron? (c) Explain briefly, using the photon model, why this time lag is not observed.

Guilherme Barros

Guilherme Barros

Numerade Educator

Problem 81

A hydrogen atom in its ground state absorbs a $97-\mathrm{nm}$ ultraviolet photon. It then emits one or more photons to return to the ground state. (a) If the atom is at rest before absorbing the UV photon, what is its recoil speed after absorption? (b) There are several different possible ways for the atom to return to the ground state. How many? (c) For each of the possibilities in
(b), give the wavelength of each photon emitted, and classify it as visible, UV, IR, x-ray, etc.

Guilherme Barros

Guilherme Barros

Numerade Educator

Problem 82

The photoelectric effect is studied using a tungsten target. The work function of tungsten is $4.5 \mathrm{eV}$. The incident photons have energy $4.8 \mathrm{eV} .$ (a) What is the threshold frequency? (b) What is the stopping potential? (c) Explain why, in classical physics, no threshold frequency is expected.

Guilherme Barros

Guilherme Barros

Numerade Educator

Problem 83

An x-ray photon with wavelength $6.00 \mathrm{pm}$ collides with a free electron initially at rest. What is the maximum possible kinetic energy acquired by the electron?

Guilherme Barros

Guilherme Barros

Numerade Educator

Problem 84

A photoelectric effect experiment is performed with tungsten. The work function for tungsten is $4.5 \mathrm{eV}$.
(a) If ultraviolet light of wavelength $0.20 \mu \mathrm{m}$ is incident on the tungsten, calculate the stopping potential.
(b) If the stopping potential is turned off (i.e., the cathode and anode are at the same voltage), the $0.20-\mu \mathrm{m}$ incident light produces a photocurrent of $3.7 \mu \mathrm{A}$. What is the photocurrent if the incident light has wavelength $400 \mathrm{~nm}$ and the same intensity as before?

Guilherme Barros

Guilherme Barros

Numerade Educator

Problem 85

In a television tube, electrons of kinetic energy $2.0 \mathrm{keV}$ strike the screen. No EM radiation is emitted below a certain wavelength. Calculate this wavelength.

Guilherme Barros

Guilherme Barros

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Problem 86

The Lyman series in the hydrogen emission spectrum is formed by electron transitions from an excited state to the ground state. Calculate the longest three wavelengths in the Lyman series.

Guilherme Barros

Guilherme Barros

Numerade Educator

Problem 87

Photons of energy $E=4.000 \mathrm{keV}$ undergo Compton scattering. What is the largest possible change in photon energy, measured as a fraction of the incident photon's energy $\left(E-E^{\prime}\right) / E ?$

Guilherme Barros

Guilherme Barros

Numerade Educator

Problem 88

Consider the emission spectrum of singly ionized helium $\left(\mathrm{He}^{+}\right)$. Find the longest three wavelengths for the series in which the electron makes a transition from a higher excited state to the first excited state (not the ground state).

Narayan Hari

Numerade Educator

Problem 89

Suppose that you have a glass tube filled with atomic hydrogen gas $\left(\mathrm{H}\right.$, not $\mathrm{H}_{2}$ ). Assume that the atoms start out in their ground states. You illuminate the gas with monochromatic light of various wavelengths, ranging through the entire IR, visible, and UV parts of the spectrum. At some wavelengths, visible light is emitted from the $\mathrm{H}$ atoms. (a) If there are two and only two visible wavelengths in the emitted light, what is the wavelength of the incident radiation? (b) What is the largest wavelength of incident radiation that causes the $\mathrm{H}$ atoms to emit visible light? What wavelength(s) is/are emitted for incident radiation at that wavelength? (c) For what wavelengths of incident light are hydrogen ions $\left(\mathrm{H}^{+}\right)$ formed?

Guilherme Barros

Guilherme Barros

Numerade Educator