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Essential College Physics

Andrew F. Rex, Richard Wolfson

Chapter 23

Modern Physics - all with Video Answers

Educators

Chapter Questions

01:07

Problem 1

Why was helium first observed on the Sun?

Ajay Singhal
Ajay Singhal
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01:20

Problem 2

Which has a higher temperature-a red-hot object or a white-hot one?

Ajay Singhal
Ajay Singhal
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01:41

Problem 3

What is the "ultraviolet catastrophe"? In what sense is it a "catastrophe"?

Ajay Singhal
Ajay Singhal
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01:08

Problem 4

A red laser and a blue laser emit the same number of photons each second. Which laser emits more power?

Ajay Singhal
Ajay Singhal
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01:17

Problem 5

A red laser and a blue laser have the same power. Which (if either) emits more photons per second?

Ajay Singhal
Ajay Singhal
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01:11

Problem 6

When a photon scatters from an electron initially at rest, why does the photon's wavelength increase?

Ajay Singhal
Ajay Singhal
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01:20

Problem 7

What is a metal's "work function"? Why is it different for different metals?

Ajay Singhal
Ajay Singhal
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01:18

Problem 8

Why is there a threshold frequency for photons in the photoelectric effect?

Ajay Singhal
Ajay Singhal
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01:53

Problem 9

A particular metal ejects photoelectrons when illuminated with green light but not yellow. Do you expect that photoelectrons will be ejected from this metal with (a) orange light; (b) blue light?

Ajay Singhal
Ajay Singhal
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01:34

Problem 10

From the standpoint of classical physics, why is it surprising that electrons are ejected almost immediately in a photoelectric experiment? How does quantum physics resolve this quandary?

Ajay Singhal
Ajay Singhal
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01:33

Problem 11

An electron is traveling at a high but nonrelativistic speed. If its speed doubles, what happens to its de Broglie wavelength?

Ajay Singhal
Ajay Singhal
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01:29

Problem 12

A rock is dropped from a tall building. Ignoring the effects of air resistance, how does its de Broglie wavelength vary as it falls?

Ajay Singhal
Ajay Singhal
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01:49

Problem 13

It has been estimated that the proton's lifetime is at least $10^{36}$ years. Does that suggest we can know the proton's rest energy precisely, or only approximately?

Ajay Singhal
Ajay Singhal
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01:54

Problem 14

Do baseball batters need to worry about the Heisenberg uncertainty principle when they swing at the ball?

Ajay Singhal
Ajay Singhal
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01:53

Problem 15

Speculate on how the uncertainty principle affects the notion of objectivity in science.

Ajay Singhal
Ajay Singhal
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01:49

Problem 16

Compare the relative advantages of the transmission electron microscope and the scanning electron microscope.

Ajay Singhal
Ajay Singhal
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01:01

Problem 17

How many charge quanta are there in $20 \mathrm{mC} ?$
(a) $3.2 \times 10^{16}$
(b) $1.3 \times 10^{17}$
(c) $3.2 \times 10^{17}$
(d) $1.3 \times 10^{18}$

Narayan Hari
Narayan Hari
Numerade Educator
01:02

Problem 18

How many hydrogen atoms are there in a $1-\mathrm{g}$ sample of pure hydrogen?
(a) $6.0 \times 10^{23}$
(b) $6.0 \times 10^{24}$
(c) $6.0 \times 10^{25}$
(d) $6.0 \times 10^{26}$

Narayan Hari
Narayan Hari
Numerade Educator
01:14

Problem 19

A blackbody radiates with median wavelength $2200 \mathrm{nm}$. What's its temperature?
(a) $975 \mathrm{~K}$;
(b) $1050 \mathrm{~K}$
(c) $1850 \mathrm{~K}$
(d) $3020 \mathrm{~K}$.

Narayan Hari
Narayan Hari
Numerade Educator
01:30

Problem 20

A blackbody radiates with median wavelength $2200 \mathrm{nm}$. What's its temperature?
(a) $975 \mathrm{~K}$;
(b) $1050 \mathrm{~K}$
(c) $1850 \mathrm{~K}$
(d) $3020 \mathrm{~K}$.

Ajay Singhal
Ajay Singhal
Numerade Educator
01:02

Problem 21

The energy of one quantum of 12 -GHz microwave radiation is
(a) $8.0 \times 10^{-22} \mathrm{~J}$
(b) $4.0 \times 10^{-23} \mathrm{~J}$
(c) $4.0 \times 10^{-24} \mathrm{~J}$
(d) $8.0 \times 10^{-24} \mathrm{~J}$.

Narayan Hari
Narayan Hari
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01:44

Problem 22

A $50-\mathrm{mW}$ laser produces 532 -nm green light. The number of photons it emits each second is (a) $1.3 \times 10^{17}$;
(b) $1.6 \times 10^{17}$
(c) $2.7 \times 10^{17}$
(d) $2.7 \times 10^{18}$.

Narayan Hari
Narayan Hari
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01:23

Problem 23

Silver's work function is $4.64 \mathrm{eV} .$ The longest waveleng th that will eject photoelectrons from silver is
(a) $535 \mathrm{nm}$;
(b) $400 \mathrm{nm}$
(c) $361 \mathrm{nm}$
(d) $267 \mathrm{nm}$.

Narayan Hari
Narayan Hari
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01:08

Problem 24

What's the energy of a photon with wavelength $590 \mathrm{nm} ?$
(a) $1.1 \mathrm{eV}$
(b) $2.1 \mathrm{eV}$
(c) $4.2 \mathrm{eV}$
(d) $5.8 \mathrm{eV}$

Narayan Hari
Narayan Hari
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01:07

Problem 25

What's the energy of a photon with wavelength $590 \mathrm{nm}$ ?
(a) $1.1 \mathrm{eV}$
(b) $2.1 \mathrm{eV}$
(c) $4.2 \mathrm{eV}$
(d) $5.8 \mathrm{eV}$

Narayan Hari
Narayan Hari
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01:10

Problem 26

An x-ray photon with wavelength 2.98 pm scatters from a stationary electron, deflecting through a $55^{\circ}$ angle. What's the wavelength of the scattered photon?
(a) $3.06 \times 10^{-3} \mathrm{nm}$
(b) $3.57 \times 10^{-3} \mathrm{nm}$
(c) $4.02 \times 10^{-3} \mathrm{nm}$
(d) $4.56 \times 10^{-3} \mathrm{nm}$

Narayan Hari
Narayan Hari
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01:08

Problem 27

If they're all traveling at the same speed, which particle has the shortest de Broglie wavelength? (a) proton; (b) neutron; (c) electron; (d) alpha particle.

Ajay Singhal
Ajay Singhal
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01:23

Problem 28

Electrons in an electron microscope must have de Broglie wavelengths of $0.45 \mathrm{nm}$. What's the electrons' speed?
(a) $5.6 \times$ $10^{5} \mathrm{~m} / \mathrm{s} ;$ (b) $1.6 \times 10^{6} \mathrm{~m} / \mathrm{s} ;$ (c) $7.2 \times 10^{6} \mathrm{~m} / \mathrm{s} ;$ (d) very close to the speed of light.

Narayan Hari
Narayan Hari
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01:01

Problem 29

How many quanta of charge are present in (a) $1 \mathrm{C} ;$ (b) $1 \mu \mathrm{C} ?$

Narayan Hari
Narayan Hari
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01:03

Problem 30

A toy balloon is filled with helium gas (He) at 1 atm and $20^{\circ} \mathrm{C}$. If the volume of the balloon is $0.027 \mathrm{~m}^{3},$ how many atoms does it contain?

Narayan Hari
Narayan Hari
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01:53

Problem 31

You have a piece of solid iron containing 2.50 moles of atoms. (a) What's its mass? (b) Suppose one atom in $10^{12}$ were missing one electron. What would be the net charge on the iron? Would you notice this if you touched the iron?

Narayan Hari
Narayan Hari
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01:03

Problem 32

An antiproton is similar to a proton, but with charge $-e$. What are the charges on the three quarks that form an antiproton?

Ajay Singhal
Ajay Singhal
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01:06

Problem 33

Radiation from a blackbody has its Wien peak at $1270 \mathrm{nm} .$ What's the blackbody's temperature?

Narayan Hari
Narayan Hari
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01:54

Problem 34

A piece of iron is heated to $600^{\circ} \mathrm{C}$.
(a) What is the median wavelength of its blackbody radiation?
(b) What temperature would give a median wavelength of half of what you found in part (a)?

Ajay Singhal
Ajay Singhal
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01:04

Problem 35

Find the surface temperature of a star whose Wien peak is in the near ultraviolet, with $\lambda=390 \mathrm{nm}$.

Narayan Hari
Narayan Hari
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01:20

Problem 36

A red giant star has surface temperature $3100 \mathrm{~K}$. What's the median wavelength in its blackbody spectrum? Compare with the Sun (see Making the Connection in Example 23.1 ).

Ajay Singhal
Ajay Singhal
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01:51

Problem 37

The tungsten lightbulb filament operates at about $3000 \mathrm{~K}$ (not far below tungsten's melting point). (a) What's the median wavelength it emits, and in what region of the spectrum does this lie? (b) If it's a 100 -W bulb, what's the filament's surface area?

Ajay Singhal
Ajay Singhal
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01:12

Problem 38

A white dwarf star has surface temperature $20 \mathrm{kK}$. (a) Where's the Wien peak in this star's blackbody curve? (b) In what part of the electromagnetic spectrum is that peak?

Ajay Singhal
Ajay Singhal
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01:39

Problem 39

In the 1960 s astronomers detected blackbody radiation with Wien peak at $1.06 \mathrm{~mm}$, apparently coming from everywhere in space. What's the temperature of the radiation source? (This "cosmic microwave background" radiation was key to understanding the evolution of the universe.)

Ajay Singhal
Ajay Singhal
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04:33

Problem 40

A blue supergiant star has surface temperature $30 \mathrm{kK}$ and has total power output 100,000 times that of the Sun. (a) Where is the Wien peak of this star's blackbody curve? (b) Why does the star appear blue? (c) Given the Sun's $6.96 \times 10^{8} \mathrm{~m}$ radius, what's the radius of the supergiant?

Umar Sohail Qureshi
Umar Sohail Qureshi
Numerade Educator
01:24

Problem 41

An 800 -K blackbody emits $450 \mathrm{~W}$ of radiation. At what temperature will the radiated power double to $900 \mathrm{~W} ?$

Ajay Singhal
Ajay Singhal
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02:08

Problem 42

A photoelectric experiment uses $265-\mathrm{nm}$ light and a silver target. Find (a) the maximum kinetic energy of the photoelectrons and (b) the stopping potential.

Ajay Singhal
Ajay Singhal
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01:35

Problem 43

Find the threshold frequency and wavelength for production of photoelectrons from a lead target.

Ajay Singhal
Ajay Singhal
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01:43

Problem 44

What's the longest wavelength that will produce photoelectrons from iron? In what part of the electromagnetic spectrum is this?

Ajay Singhal
Ajay Singhal
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02:08

Problem 45

(a) What are the threshold frequency and wavelength for photons from a silver target? (b) What's the stopping potential for photoelectrons from silver under 135 -nm ultraviolet light?

Ajay Singhal
Ajay Singhal
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01:46

Problem 46

Suppose you want to produce photoelectrons with kinetic energy $1.50 \mathrm{eV}$ from a copper target. What wavelength of electromagnetic radiation should you use?

Narayan Hari
Narayan Hari
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02:40

Problem 47

A sodium target is illuminated with $442-\mathrm{nm}$ violet light. Find (a) the stopping potential for the photoelectrons produced and
(b) the photoelectrons' maximum speed.

Ajay Singhal
Ajay Singhal
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02:06

Problem 48

Of the elements in Table $23.1,$ which can produce photoelectrons when illuminated with visible light?

Ajay Singhal
Ajay Singhal
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05:20

Problem 49

Photoelectrons from a metal target have a $1.20-\mathrm{V}$ stopping potential when the target is illuminated with $340-\mathrm{nm}$ ultraviolet radiation. Find (a) the stopping potential for the same target under 260 -nm radiation and (b) the work function for this metal.

Umar Sohail Qureshi
Umar Sohail Qureshi
Numerade Educator
02:15

Problem 50

A $1.0-\mathrm{mW}$ laser with a $405-\mathrm{nm}$ wavelength illuminates a sodium target. If 1 in $10^{5}$ incident photons generates a photoelectron, what's the photocurrent?

Ajay Singhal
Ajay Singhal
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03:39

Problem 51

In an experiment to measure Planck's constant, a metal target is illuminated with ultraviolet light. When the wavelength is $300 \mathrm{nm},$ the measured stopping potential is $1.10 \mathrm{~V}$. When the wavelength is changed to $200 \mathrm{nm}$, the stopping potential becomes $3.06 \mathrm{~V}$. (a) What value does this experiment yield for Planck's constant? What's the percent error from the accepted value of $h ?$ (b) Using the experimental value $h,$ find the threshold frequency and work function for this metal.

Ren Jie Tuieng
Ren Jie Tuieng
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01:10

Problem 52

An x-ray photon with wavelength 1.94 pm scatters from a stationary electron, deflecting through an angle of $105^{\circ} .$ What's the scattered photon's wavelength?

Narayan Hari
Narayan Hari
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01:29

Problem 53

Find the energy of one quantum of microwave radiation with frequency (a) $1 \mathrm{GHz}$ and (b) $300 \mathrm{GHz}$.

Narayan Hari
Narayan Hari
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01:28

Problem 54

When perceiving 630 -nm red light, your unaided eye can barely detect light at a threshold power around $2.5 \times 10^{-15} \mathrm{~W}$. At what rate are photons entering your eye at this level?

Narayan Hari
Narayan Hari
Numerade Educator
01:32

Problem 55

A semiconductor laser produces a continuous 10.0 -W beam with wavelength $2.4 \mu \mathrm{m}$. Find (a) the energy of each photon and
(b) the number of photons emitted each second.

Ajay Singhal
Ajay Singhal
Numerade Educator
02:30

Problem 56

(a) Find the wavelength of a 4.1 -eV photon. In what part of the electromagnetic spectrum is this? Repeat for photons with energies (b) $2.3 \mathrm{eV}$ and $(\mathrm{c}) 0.69 \mathrm{eV}$

Ajay Singhal
Ajay Singhal
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04:37

Problem 57

While sitting in direct sunlight, you absorb UVB radiation with average wavelength $310 \mathrm{nm}$. (a) Find the energy of an average UVB photon, and compare with an average visible photon $(\lambda=550 \mathrm{nm})$. (b) How many photons are in $1 \mathrm{~J}$ of energy at each wavelength?

Umar Sohail Qureshi
Umar Sohail Qureshi
Numerade Educator
01:24

Problem 58

A medical x-ray beam has wavelength $1.26 \mathrm{nm}$. (a) What's the energy of one photon in this beam? (b) How many photons are in a typical chest x-ray dose that delivers 0.021 J of energy?

Narayan Hari
Narayan Hari
Numerade Educator
02:48

Problem 59

Example 23.3 showed that the Sun emits energy at the rate of about $3.9 \times 10^{26} \mathrm{~W}$. (a) Using the astronomical data in Appendix E, estimate the fraction of this energy that falls on Earth. (b) With the Sun directly overhead, what's the rate at which energy strikes each square meter of Earth's surface? (Ignore reflection and absorption by the atmosphere.) (c) Discuss the implications of your answer in part (b) for solar energy use.

Carlos Henrique De Lima
Carlos Henrique De Lima
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07:42

Problem 60

A $639 \mathrm{keV}$ x-ray photon scatters from an electron at rest, deflecting through $105^{\circ} .$ What is the scattered photon's energy?

Umar Sohail Qureshi
Umar Sohail Qureshi
Numerade Educator
01:05

Problem 61

You're studying Compton scattering using $x$ rays with wave-length equal to the Compton wavelength. At what scattering angle will you observe $x$ rays with a wavelength twice that of the incident x rays?

Ajay Singhal
Ajay Singhal
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03:17

Problem 62

A photon with a wavelength 4.50 pm scatters from an electron initially at rest. Find (a) the maximum kinetic energy for the scattered electron and (b) the wavelength of the scattered photon when the scattered electron has its maximum kinetic energy.

Ajay Singhal
Ajay Singhal
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01:02

Problem 63

X rays with wavelength 5.0 pm scatter from electrons, recoiling with wavelength $8.2 \mathrm{pm}$. What's the scattering angle?

Ajay Singhal
Ajay Singhal
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06:41

Problem 64

Compton scattering can occur from atoms as well as from electrons. If photons scatter from atoms of helium (He) gas, what's their maximum wavelength change? Should the photon energies be larger or smaller than those used in Compton scattering by electrons?

Umar Sohail Qureshi
Umar Sohail Qureshi
Numerade Educator
01:24

Problem 65

Your Compton-effect instrumentation can detect a $5.0 \%$ change in the photon's wavelength. What's the maximum initial photon wavelength in this case?

Ajay Singhal
Ajay Singhal
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07:29

Problem 66

A hydrogen atom initially at rest emits a $434-\mathrm{nm}$ photon. Find (a) the photon's energy and momentum, (b) the momentum of the atom after emitting the photon, and (c) the kinetic energy of the recoiling atom. Compare with the photon's energy.

Umar Sohail Qureshi
Umar Sohail Qureshi
Numerade Educator
04:38

Problem 67

(a) Find the energy needed to produce a proton-antiproton pair. (b) Find the energies of the two photons produced when a proton and antiproton at rest annihilate.

Umar Sohail Qureshi
Umar Sohail Qureshi
Numerade Educator
04:18

Problem 68

In a colliding-beam experiment, an electron and positron traveling at the same speeds but opposite directions collide, producing two photons. If each of the photons has energy equal to three times the electron's rest energy, what were the electron and positron speeds?

Umar Sohail Qureshi
Umar Sohail Qureshi
Numerade Educator
02:00

Problem 69

Find (a) the speed of an electron with de Broglie wavelength $1.0 \mathrm{nm}$ and $(\mathrm{b})$ the de Broglie wavelength of a proton with that speed.

Narayan Hari
Narayan Hari
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01:01

Problem 70

The electrons in an electron microscope have speed of $4.0 \mathrm{Mm} / \mathrm{s}$. Find their de Broglie wavelength.

Narayan Hari
Narayan Hari
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01:01

Problem 71

An electron microscope calls for electrons with de Broglie wavelength $0.25 \mathrm{nm}$. What's the electrons' speed?

Narayan Hari
Narayan Hari
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01:34

Problem 72

In an undergraduate version of the Davisson-Germer experiment, electrons are accelerated through several potential differences. For each potential difference, find the corresponding de Broglie wavelength and electron speed: (a) $12 \mathrm{~V} ;$ (b) $30 \mathrm{~V}$; (c) $60 \mathrm{~V}$.

Ajay Singhal
Ajay Singhal
Numerade Educator
07:32

Problem 73

Find the kinetic energy of each of the following particles, each having de Broglie wavelength $0.30 \mathrm{nm}:$ (a) electrons;
(b) neutrons; (c) alpha particles.

Umar Sohail Qureshi
Umar Sohail Qureshi
Numerade Educator
07:44

Problem 74

Suppose you want to observe neutron diffraction in a crystal with 0.29 -nm spacing between lattice planes.
(a) Find the momentum and kinetic energy of neutrons having wavelength equal to this spacing.
(b) If these neutrons constituted an ideal gas, what would be the gas temperature? Explain why these are called "cold" neutrons.

Umar Sohail Qureshi
Umar Sohail Qureshi
Numerade Educator
01:27

Problem 75

What's the de Broglie wavelength of a nitrogen $\left(\mathrm{N}_{2}\right)$ molecule in air at room temperature $(293 \mathrm{~K})$ ? How likely is it that you'll be able to observe diffraction effects in such molecules?

Ajay Singhal
Ajay Singhal
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01:50

Problem 76

A 25-g marble passes through a 2.0-cm-wide opening. What should be the marble's speed in order for it to experience a $0.1^{\circ}$ diffraction angle through the opening? (Assume first-order single-slit diffraction.)

Ajay Singhal
Ajay Singhal
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01:56

Problem 77

(a) What's the kinetic energy of an electron having de Broglie wavelength $400 \mathrm{nm}$ ? (b) Compare with the energy of a photon having the same wavelength.

Ajay Singhal
Ajay Singhal
Numerade Educator
02:01

Problem 78

If you want to measure the position of a $142-\mathrm{g}$ baseball moving at $25 \mathrm{~m} / \mathrm{s}$ to within $1.0 \mu \mathrm{m}$, what's the corresponding uncertainty in its speed? Do you think you can really measure the speed with that precision?

Narayan Hari
Narayan Hari
Numerade Educator
08:42

Problem 79

An electron is confined to a box the size of a small atom, $0.10 \mathrm{nm}$ across. (a) What's the uncertainty in the electron's momentum? (b) Suppose the momentum is just equal to the minimum uncertainty value you computed in part (a). What's the electron's energy? What wavelength photon would have the same energy?

Umar Sohail Qureshi
Umar Sohail Qureshi
Numerade Educator
01:05

Problem 80

The $\mathrm{W}^{+}$ is an elementary particle with rest energy around $80 \mathrm{GeV},$ uncertain by about $2.1 \mathrm{GeV}$. Use Heisenberg's uncertainty principle to estimate this particle's minimum lifetime. When a particle is moving with a relativistic speed, its de Broglie wavelength is still $\lambda=h / p,$ where $p$ is the relativistic momentum. Use this fact in the following problems.

Narayan Hari
Narayan Hari
Numerade Educator
02:17

Problem 81

Find the de Broglie wavelength of an electron moving at (a) $0.10 c ;$ (b) $0.50 c$; (c) $0.99 c$.

Ajay Singhal
Ajay Singhal
Numerade Educator
08:46

Problem 82

In a certain electron microscope, a de Broglie wavelength of $0.015 \mathrm{nm}$ is required. Find the potential difference required to accelerate electrons to the proper speed.

Umar Sohail Qureshi
Umar Sohail Qureshi
Numerade Educator
06:11

Problem 83

The Stanford linear accelerator can accelerate electrons to kinetic energies of $50 \mathrm{GeV}$. What's the de Broglie wavelength of these electrons? Compare with the diameter of a proton, about $2 \mathrm{fm}$

Umar Sohail Qureshi
Umar Sohail Qureshi
Numerade Educator
07:34

Problem 84

In his double-slit experiment with electrons, Jönsson used electrons with kinetic energy $50 \mathrm{keV}$. (a) Find the electrons' de Broglie wavelength. (b) The two slits were separated by $2.0 \mu \mathrm{m}$. On a screen $0.350 \mathrm{~m}$ from the slits, what was the distance between bright diffraction fringes?

SB
Sarah Brandsen
Numerade Educator
02:15

Problem 85

(a) Find the Compton wavelength of a proton. (b) Find the energy (in eV) of a gamma ray whose wavelength equals the proton's Compton wavelength.

Ajay Singhal
Ajay Singhal
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01:22

Problem 86

Electrons in a photoelectric experiment emerge from an aluminum surface with a maximum kinetic energy of $1.3 \mathrm{eV}$. What is the wavelength of the incident radiation?

Narayan Hari
Narayan Hari
Numerade Educator
01:03

Problem 87

The most energetic cosmic rays ever detected are photons with energies approaching $10 \mathrm{~J}$. Find the wavelength of such a photon.

Narayan Hari
Narayan Hari
Numerade Educator
04:15

Problem 88

A cosmic ray interacts for a mere $12 \mathrm{fs}$ with its detector. Having just learned about the uncertainty principle, you realize that this interaction time establishes a precision limit on measurement of cosmic-ray energy. Find (a) the minimum uncertainty in that energy and (b) the fractional uncertainty for a 4.5 -MeV cosmic ray.

Umar Sohail Qureshi
Umar Sohail Qureshi
Numerade Educator
02:52

Problem 89

An electron is initially at rest. What will be its kinetic energy after a 0.10 -nm x-ray photon scatters from it at $90^{\circ}$ to its original direction?

Ajay Singhal
Ajay Singhal
Numerade Educator
03:19

Problem 90

A photocathode emits electrons with maximum kinetic energy $0.85 \mathrm{eV}$ when illuminated with 430 -nm violet light. (a) Will it eject electrons under $633-\mathrm{nm}$ red light? (b) Find the threshold wavelength for this material.

Ajay Singhal
Ajay Singhal
Numerade Educator
08:41

Problem 91

(a) Estimate the number of photons per second emitted by a 100 -W lightbulb, assuming a photon wavelength in the middle of the visible spectrum, $550 \mathrm{nm}$.
(b) A person can just see this bulb from a distance of $800 \mathrm{~m}$, with the pupil diameter dilated to $7.5 \mathrm{~mm}$. How many photons per second are entering the pupil?

Umar Sohail Qureshi
Umar Sohail Qureshi
Numerade Educator