Deck 28: Quantum Physics

Question 1

Monochromatic light falls on a metal surface and electrons are ejected. If the intensity of the light is increased, what will happen to the ejection rate and maximum energy of the electrons?

A)greater rate; same maximum energy.
B)same rate; greater maximum energy.
C)greater rate; greater maximum energy.
D)same rate; same maximum energy.

Answer 1

A

Question 2

If the wavelength of a photon in vacuum is the same as the de Broglie wavelength of an electron, which one is traveling faster through space?

A)The electron because it has more mass.
B)The photon because photons always travel through space faster than electrons.
C)They both have the same speed.

Answer 2

B

Question 3

A researcher is using x-rays to investigating a cubic crystal. He is looking at Bragg reflection from the planes parallel to the cube faces. He finds that when using x-rays with a wavelength of 0.165 nm, a strong first maximum occurs when the beam makes an angle of 23.5° with the planes. What is the spacing of adjacent atoms in this crystal?

Answer 3

0.207 nm

Question 4

If a proton and an electron have the same de Broglie wavelengths, which one is moving faster?

A)the electron
B)the proton
C)They both have the same speed.

Question 5

Light of a given wavelength is used to illuminate the surface of a metal, however, no photoelectrons are emitted. In order to cause electrons to be ejected from the surface of this metal you should

A)use light of a longer wavelength.
B)use light of a shorter wavelength.
C)use light of the same wavelength but increase its intensity.
D)use light of the same wavelength but decrease its intensity.

Question 6

A beam of light falling on a metal surface is causing electrons to be ejected from the surface. If we now double the frequency of the light, which of the following statements are correct? (There could be more than one correct choice.)

A)The kinetic energy of the ejected electrons doubles.
B)The speed of the ejected electrons doubles.
C)The number of electrons ejected per second doubles.
D)Twice as many photons hit the metal surface as before.
E)None of the above things occur.

Question 7

If the maximum possible accuracy in measuring the velocity of a particle increases, the maximum possible accuracy in measuring its position will

A)increase.
B)decrease.
C)not be affected.

Question 8

Two sources emit beams of microwaves. The microwaves from source A have a frequency of 10 GHz, and the ones from source B have a frequency of 20 GHz. This is all we know about the two beams. Which of the following statements about these beams are correct? (There could be more than one correct choice.)

A)Beam B carries twice as many photons per second as beam A.
B)A photon in beam B has twice the energy of a photon in beam A.
C)The intensity of beam B is twice as great as the intensity of beam A.
D)A photon in beam B has the same energy as a photon in beam A.
E)None of the above statements are true.

Question 9

If the maximum possible accuracy in measuring the position of a particle increases, the maximum possible accuracy in measuring its velocity will

A)increase.
B)decrease.
C)not be affected.

Question 10

A proton and an electron are both accelerated to the same final kinetic energy. If λ_p is the de Broglie wavelength of the proton and λ_e is the de Broglie wavelength of the electron, then

A)λ_p > λ_e.
B)λ_p = λ_e.
C)λ_p < λ_e.

Question 11

Which of the following actions will increase the de Broglie wavelength of a speck of dust? (There could be more than one correct choice.)

A)Increase its mass.
B)Increase its speed.
C)Decrease its mass.
D)Decrease its speed.
E)Decrease its momentum.

Question 12

Two sources emit beams of light of wavelength 550 nm. The light from source A has an intensity of 10 µW/m², and the light from source B has an intensity of 20 µW/m². This is all we know about the two beams. Which of the following statements about these beams are correct? (There could be more than one correct choice.)

A)Beam B carries twice as many photons per second as beam A.
B)A photon in beam B has twice the energy of a photon in beam A.
C)The frequency of the light in beam B is twice as great as the frequency of the light in beam A.
D)A photon in beam B has the same energy as a photon in beam A.
E)None of the above statements are true.

Question 13

A proton and an electron are both accelerated to the same final speed. If λ_p is the de Broglie wavelength of the proton and λ_e is the de Broglie wavelength of the electron, then

A)λ_p > λ_e.
B)λ_p = λ_e.
C)λ_p < λ_e.

Question 14

When the surface of a metal is exposed to blue light, electrons are emitted. If the intensity of the blue light is increased, which of the following things will also increase?

A)the number of electrons ejected per second
B)the maximum kinetic energy of the ejected electrons
C)the time lag between the onset of the absorption of light and the ejection of electrons
D)the work function of the metal
E)all of the above

Question 15

A blue laser beam is incident on a metallic surface, causing electrons to be ejected from the metal. If the frequency of the laser beam is increased while the intensity of the beam is held fixed,

A)the rate of ejected electrons will decrease and their maximum kinetic energy will increase.
B)the rate of ejected electrons will remain the same but their maximum kinetic energy will increase.
C)the rate of ejected electrons will increase and their maximum kinetic energy will increase.
D)the rate of ejected electrons will remain the same but their maximum kinetic energy will decrease.

Question 16

Protons are being accelerated in a particle accelerator. When the speed of the protons is doubled, their de Broglie wavelength will

A)increase by a factor of 4.
B)increase by a factor of 2.
C)decrease by a factor of 2.
D)increase by a factor of $\sqrt { 2 }$ .
E)decrease by a factor of $\sqrt { 2 }$ .

Question 17

Certain planes of a crystal of halite have a spacing of 0.399 nm. The crystal is irradiated by a beam of x-rays. First order constructive interference occurs when the beam makes an angle of 20° with the planes of the crystal surface. What is the wavelength of the x-rays?

A)0.14 nm
B)0.17 nm
C)0.21 nm
D)0.24 nm
E)0.27 nm

Question 18

Monochromatic light is incident on a metal surface, and the ejected electrons give rise to a current in the circuit shown in the figure. The maximum kinetic energy of the ejected electrons is determined by applying a reverse ('stopping')potential, sufficient to reduce the current in the ammeter to zero. If the intensity of the incident light is increased, how will the required stopping potential change?

A)It will remain unchanged.
B)It will increase.
C)It will decrease.

Question 19

If a proton and an electron have the same speed, which one has the longer de Broglie wavelength?

A)the electron
B)the proton
C)It is the same for both of them.

Question 20

Protons are being accelerated in a particle accelerator. When the energy of the protons is doubled, their de Broglie wavelength will

A)increase by a factor of 4.
B)increase by a factor of 2.
C)decrease by a factor of 2.
D)increase by a factor of $\sqrt { 2 }$ .
E)decrease by a factor of $\sqrt { 2 }$ .

Question 21

A metallic surface is illuminated with light of wavelength 400 nm. If the work function for this metal is 2.40 eV, what is the maximum kinetic energy of the ejected electrons, in electron-volts? (1 eV = 1.60 × 10^-19 J, c = 3.00 × 10⁸ m/s, h = 6.626 × 10^-34 J ? s)

Question 22

A laser pulse of duration 25 ms has a total energy of 1.4 J. If the wavelength of this radiation is 567 nm, how many photons are emitted in one pulse? (c = 3.00 × 10⁸ m/s, h = 6.626 × 10^-34 J ∙ s)

A)4.0 × 10¹⁸
B)9.9 × 10¹⁹
C)4.8 × 10¹⁹
D)1.6 × 10¹⁷
E)3.2 × 10¹⁷

Question 23

For what wavelength does a 100-mW laser beam deliver 1.6 × 10¹⁷ photons in one second? (c = 3.0 × 10⁸ m/s, h = 6.626 × 10^-34 J ∙ s)

A)320 nm
B)330 nm
C)340 nm
D)350 nm

Question 24

A metal has a work function of 4.50 eV. Find the maximum kinetic energy of the photoelectrons if light of wavelength 250 nm shines on the metal. (1 eV = 1.60 × 10^-19 J, c = 3.00 × 10⁸ m/s, h = 6.626 × 10^-34 J ∙ s)

A)0.00 eV
B)0.37 eV
C)0.47 eV
D)0.53 eV

Question 25

Gamma rays are photons with very high energy. What is the wavelength of a gamma-ray photon with energy 7.7 × 10^-13 J? (c = 3.0 × 10⁸ m/s, h = 6.626 × 10^-34 J ∙ s)

A)2.6 × 10^-13 m
B)3.9 × 10^-13 m
C)3.1 × 10^-13 m
D)3.5 × 10^-13 m

Question 26

A laser emits a pulse of light that lasts 10 ns. The light has a wavelength of 690 nm, and each pulse has an energy of 480 mJ. How many photons are emitted in each pulse? (c = 3.0 × 10⁸ m/s, h = 6.626 × 10^-34 J ? s)

A)1.7 × 10¹⁸
B)2.1 × $10 ^ { 27 }$
C)2.6 × $10 ^ { 37 }$
D)3.1 × $10^{43}$

Question 27

An 84-kW AM radio station broadcasts at 1000 kHz. How many photons are emitted each second by the transmitting antenna? (h = 6.626 × 10^-34 J ? s)

A)1.3 × $10 ^ { 32 }$
B)2.9 × $10 ^ { 24 }$
C)6.3 × $10 ^ { 12 }$
D)1.4 × $10^{15}$

Question 28

A metal surface has a work function of 2.50 eV. What is the longest wavelength of light that will eject electrons from the surface of this metal? (1 eV = 1.60 × 10^-19 J, c = 3.00 × 10⁸ m/s, h = 6.626 × 10^-34 J ? s)

Question 29

The work function of a particular metal is $4.20 \times 10 ^ { - 19 } \mathrm {~J}$ What is the photoelectric cutoff (threshold)wavelength for this metal? (c = 3.00 × 10⁸ m/s, h = 6.626 × 10^-34 J ? s)

A)473 nm
B)308 nm
C)393 nm
D)554 nm

Question 30

A helium-neon laser emits light at 632.8 nm. If the laser emits $1.82 \times 10 ^ { 17 }$ photons/second, what is its power output in mW? (c = 3.00 × 10⁸ m/s, h = 6.626 × 10^-34 J ? s)

A)57.2 mW
B)28.6 mW
C)37.2 mW
D)45.7 mW

Question 31

Certain planes of a crystal of halite have a spacing of 0.399 nm. The crystal is irradiated by a beam of x-rays. First order constructive interference occurs when the beam makes an angle of 20° with the planes of the crystal surface. What angle does the beam make with the crystal planes for second order constructive?

A)37°
B)40°
C)43°
D)46°
E)49°

Question 32

A crystal is irradiated with x-rays with a wavelength of 0.120 nm. The atomic planes in the crystal are separated by 0.21 nm. At what angles of incidence with respect to the normal will the x-rays reflect from the crystal?

A)73°, 55°, 31°
B)only 55°
C)only 73° and 31°
D)only 73°

Question 33

If the longest wavelength of light that is able to dislodge electrons from a metal is 373 nm, what is the work function of that metal, in electron-volts? (1 eV = 1.60 × 10^-19 J, c = 3.00 × 10⁸ m/s, h = 6.626 × 10^-34 J ? s)

Question 34

A photoelectric surface has a work function of 2.10 eV. Calculate the maximum kinetic energy, in eV, of electrons ejected from this surface by electromagnetic radiation of wavelength 356 nm. (1 eV = 1.60 × 10^-19 J, c = 3.00 × 10⁸ m/s, h = 6.626 × 10^-34 J ? s)

Question 35

What is the cutoff (threshold)frequency for a metal surface that has a work function of 5.42 eV? (1 eV = 1.60 × 10^-19 J, h = 6.626 × 10^-34 J ? s)

A)1.31 × $10^{15}$ Hz
B)2.01 × $10^{15}$ Hz
C)3.01 × $10^{15}$ Hz
D)5.02 × $10^{15}$ Hz
E)6.04 × $10^{15}$ Hz

Question 36

The work function of a certain metal is 1.90 eV. What is the longest wavelength of light that can cause photoelectron emission from this metal? (1 eV = 1.60 × 10^-19 J, c = 3.00 × 10⁸ m/s, h = 6.626 × 10^-34 J ∙ s)

A)231 nm
B)14.0 nm
C)62.4 nm
D)344 nm
E)654 nm

Question 37

Gamma rays are photons with very high energy. How many visible-light photons with a wavelength of 500 nm would you need to equal the energy of a gamma-ray photon with energy $4.1 \times 10 ^ { - 13 } \mathrm {~J} ?$

A)1.0 × 10⁶
B)1.4 × 10⁸
C)6.2 × 10⁹
D)3.9 × 10³

Question 38

What is the longest wavelength of light that can cause photoelectron emission from a metal that has a work function of 2.20 eV? (1 eV = 1.60 × 10^-19 J, c = 3.00 × 10⁸ m/s, h = 6.626 × 10^-34 J ∙ s)

A)417 nm
B)257 nm
C)344 nm
D)565 nm
E)610 nm

Question 39

The lattice spacing of the principal Bragg planes in sodium chloride is 0.282 nm. For what wavelength of x-rays will the first order reflected beam diffract at 55° with respect to the normal to the crystal planes?

A)0.323 nm
B)0.530 nm
C)0.662 nm
D)0.150 nm
E)0.462 nm

Question 40

What is the wavelength of a 6.32-eV photon? (c = 3.00 × 10⁸ m/s, h = 6.626 × 10^-34 J ∙ s, 1 eV = 1.60 × 10^-19 J)

A)197 nm
B)167 nm
C)216 nm
D)234 nm

Question 41

When a photoelectric surface is illuminated with light of wavelength 437 nm, the stopping potential is measured to be 1.67 V. (1 eV = 1.60 × 10^-19 J, e = 1.60 × 10^-19 C, m_electron = 9.11 × 10^-31 kg, h = 6.626 × 10^-34 J ? s)
(a)What is the work function of the metal, in eV?
(b)What is the maximum speed of the ejected electrons?

Question 42

A photocathode having a work function of 2.8 eV is illuminated with monochromatic electromagnetic radiation whose photon energy is 4.0 eV. What is the threshold (cutoff)frequency for photoelectron production? (1 eV = 1.60 × 10^-19 J, h = 6.626 × 10^-34 J ∙ s)

A)6.8 × 10¹⁴ _Hz
B)2.9 × 10¹⁴ _Hz
C)7.7 × 10¹⁴ _Hz
D)8.6 × 10¹⁴ _Hz
E)9.7 × 10¹⁴ _Hz

Question 43

If the work function of a metal surface is 2.20 eV, what frequency of incident light would give a maximum kinetic energy of 0.25 eV to the photoelectrons ejected from this surface? (1 eV = 1.60 × 10^-19 J, h = 6.626 × 10^-34 J ∙ s)

A)2.05 × 10¹⁴ Hz
B)1.02 × 10¹⁴ Hz
C)2.50 × 10¹⁴ Hz
D)3.53 × 10¹⁴ Hz
E)5.92 × 10¹⁴ Hz

Question 44

A beam of light with a frequency range from 3.01 × 10¹⁴ Hz to 6.10 × 10¹⁴ Hz is incident on a metal surface. If the work function of the metal surface is 2.20 eV, what is the maximum kinetic energy of photoelectrons ejected from this surface? (h = 6.626 × 10^-34 J ∙ s, 1 eV = 1.60 × 10^-19 J)

A)0.33 eV
B)0.21 eV
C)0.42 eV
D)0.16 eV
E)0.48 eV

Question 45

A photocathode that has a work function of 2.4 eV is illuminated with monochromatic light having photon energy 3.5 eV. What is the wavelength of this light? (c = 3.00 × 10⁸ m/s, h = 6.626 × 10^-34 J ∙ s, 1 eV = 1.60 × 10^-19 J)

A)350 nm
B)330 nm
C)300 nm
D)380 nm
E)410 nm

Question 46

Light with a frequency of 8.70 × 10¹⁴ Hz is incident on a metal that has a work function of 2.80 eV. What is the maximum kinetic energy that a photoelectron ejected in this process can have? (1 eV = 1.60 × 10^-19 J, h = 6.626 × 10^-34 J ∙ s)

A)8.7 × 10^-19 J
B)3.1 × 10^-19 J
C)1.3 × 10^-19 J
D)2.4 × 10^-19 J
E)4.5 × 10^-19 J

Question 47

A monochromatic light beam is incident on the surface of a metal having a work function of 2.50 eV. If a 1.0-V stopping potential is required to make the electron current zero, what is the wavelength of light? (c = 3.00 × 10⁸ m/s, h = 6.626 × 10^-34 J ∙ s, 1 eV = 1.60 × 10^-19 J)

A)355 nm
B)423 nm
C)497 nm
D)744 nm

Question 48

What is the longest wavelength of electromagnetic radiation that will eject photoelectrons from sodium metal for which the work function is 2.28 eV? (c = 3.00 × 10⁸ m/s, h = 6.626 × 10^-34 J ∙ s, 1 eV = 1.60 × 10^-19 J)

A)580 nm
B)499 nm
C)633 nm
D)668 nm
E)545 nm

Question 49

How "slow" must a 200-g ball move to have a de Broglie wavelength of 1.0 mm? (h = 6.626 × 10^-34 J ? s)

Question 50

When it is struck by 240-nm photons, a material having a work function of 2.60 eV emits electrons. What is the maximum kinetic energy of the emitted electrons? (c = 3.00 × 10⁸ m/s, h = 6.626 × 10^-34 J ∙ s, 1 eV = 1.60 × 10^-19 J)

A)2.58 eV
B)5.18 eV
C)2.00 eV
D)4.21 eV

Question 51

A photocathode whose work function is 2.9 eV is illuminated with white light that has a continuous wavelength band from 400 nm to 700 nm. What is the range of the wavelength band in this white light illumination for which photoelectrons are not produced?(c = 3.00 × 10⁸ m/s, h = 6.626 × 10^-34 J ∙ s, 1 eV = 1.60 × 10^-19 J)

A)430 nm to 700 nm
B)400 nm to 480 nm
C)430 nm to 480 nm
D)400 nm to 430 nm
E)480 nm to 700 nm

Question 52

In her physics laboratory, Mathilda shines electromagnetic radiation on a material and collects photoelectric data to determine Planck's constant. She measures a stopping potential of 5.82 V for radiation of wavelength 100 nm, and 17.99 V for radiation of wavelength 50.0 nm. (1 eV = 1.60 × 10^-19 J, c = 3.00 × 10⁸ m/s)
(a)Using Mathilda's data, what value does she determine for Planck's constant?
(b)What is the work function of the material Mathilda is using, in electron-volts?

Question 53

Light with a wavelength of 310 nm is incident on a metal that has a work function of 3.80 eV. What is the maximum kinetic energy that a photoelectron ejected in this process can have? (1 eV = 1.60 × 10^-19 J, c = 3.00 × 10⁸ m/s, h = 6.626 × 10^-34 J ∙ s)

A)0.62 × 10^-19 J
B)0.21 × 10^-19 J
C)0.36 × 10^-19 J
D)0.48 × 10^-19 J
E)0.33 × 10^-19 J

Question 54

When light of wavelength 350 nm is incident on a metal surface, the stopping potential of the photoelectrons is measured to be 0.500 V. What is the work function of this metal? (c = 3.00 × 10⁸ m/s, h = 6.626 × 10^-34 J ∙ s, 1 eV = 1.60 × 10^-19 J)

A)0.500 eV
B)3.05 eV
C)3.54 eV
D)4.12 eV

Question 55

A photocathode having a work function of 2.4 eV is illuminated with monochromatic light whose photon energy is 3.4 eV. What is maximum kinetic energy of the photoelectrons produced?(c = 3.00 × 10⁸ m/s, h = 6.626 × 10^-34 J ∙ s, 1 eV = 1.60 × 10^-19 J)

A)1.6 × 10^-19 _J
B)3.8 × 10^-19 _J
C)4.4 × 10^-19 _J
D)4.9 × 10^-19 _J
E)5.4 × 10^-19 _J

Question 56

When a metal is illuminated by light, photoelectrons are observed provided that the wavelength of the light is less than 520 nm. What is the metal's work function? (c = 3.00 × 10⁸ m/s, h = 6.626 × 10^-34 J ∙ s, 1 eV = 1.60 × 10^-19 J)

A)2.4 eV
B)2.6 eV
C)2.8 eV
D)3.0 eV

Question 57

When light of wavelength 350 nm is incident on a metal surface, the stopping potential of the photoelectrons is 0.500 V. What is the threshold (cutoff)frequency of this metal? (c = 3.00 × 10⁸ m/s, h = 6.626 × 10^-34 J ∙ s, 1 eV = 1.60 × 10^-19 J)

A)3.47 × 10¹⁴ Hz
B)3.74 × 10¹⁴ Hz
C)4.73 × 10¹⁴ Hz
D)7.36 × 10¹⁴ Hz

Question 58

When it is struck by 240-nm photons, a metal ejects electrons with a maximum kinetic energy of $2.58 \mathrm { eV }$ What is the work function of this material? (c = 3.00 × 10⁸ m/s, h = 6.626 × 10^-34 J ? s, 1 eV = 16.0 × 10^-19 J)

A)2.60 eV
B)2.18 eV
C)3.02 eV
D)3.43 eV

Question 59

Calculate the kinetic energy, in electron-volts, of a neutron that has a de Broglie wavelength of $7.2 \times 10 ^ { - 12 } \mathrm {~m}$ (m_neutron = 1.675 × 10^-27 kg, 1 eV = 1.6 × 10^-19 J, h = 6.626 × 10^-34 J ? s)

Question 60

When light of wavelength 350 nm is incident on a metal surface, the stopping potential of the photoelectrons is 0.500 V. What is the maximum kinetic energy of these electrons? (c = 3.00 × 10⁸ m/s, h = 6.626 × 10^-34 J ∙ s, 1 eV = 1.60 × 10^-19 J)

A)0.500 eV
B)3.04 eV
C)3.54 eV
D)4.12 eV

Question 61

What is the de Broglie wavelength of a ball of mass 200 g moving at 30 m/s? (h = 6.626 × 10^-34 J ∙ s)

A)1.1 × 10^-34 m
B)2.2 × 10^-34 m
C)4.5 × 10^-28 m
D)6.7 × 10^-27 m

Question 62

An electron has the same de Broglie wavelength as the wavelength of a 1.8 eV photon. What is the speed of the electron? (m_electron = 9.11 × 10^-31 kg, c = 3.00 × 10⁸ m/s, 1 eV = 1.60 × 10^-19 J)

A)1100 m/s
B)980 m/s
C)910 m/s
D)840 m/s
E)770 m/s

Question 63

What is the wavelength of the matter wave associated with a 0.50-kg ball moving at 25 m/s? (h = 6.626 × 10^-34 J ∙ s)

A)3.5 × 10^-35 m
B)5.3 × 10^-35 m
C)3.5 × 10^-33 m
D)5.3 × 10^-33 m

Question 64

After an electron has been accelerated through a potential difference of 0.15 kV, what is its de Broglie wavelength? (e = 1.60 × 10^-19 C, m_electron = 9.11 × 10^-31 kg, h = 6.626 × 10^-34 J ∙ s)

A)0.10 nm
B)1.0 nm
C)1.0 mm
D)1.0 cm

Question 65

If the momentum of an electron is 1.95 × 10^-27 kg ∙ m/s, what is its de Broglie wavelength? (h = 6.626 × 10^-34 J ∙ s)

A)340 nm
B)210 nm
C)170 nm
D)420 nm
E)520 nm

Question 66

What is the wavelength of the matter wave associated with an electron moving with a speed of 2.5 × 10⁷ m/s? (m_electron = 9.11 × 10^-31 kg, h = 6.626 × 10^-34 J ∙ s)

A)29 pm
B)35 pm
C)47 pm
D)53 pm

Question 67

If the de Broglie wavelength of an electron is 380 nm, what is the speed of this electron? (m_electron = 9.11 × 10^-31 kg, h = 6.626 × 10^-34 J ∙ s)

A)2.0 km/s
B)3.8 km/s
C)1.9 km/s
D)4.1 km/s
E)5.2 km/s

Question 68

An electron is accelerated from rest through a potential difference. After acceleration the electron has a wavelength of 880 nm. What is the potential difference responsible for the acceleration of the electron? (h = 6.626 × 10^-34 J ∙ s, m_electron = 9.11 × 10-31 kg, e = 1.6 10^-19 C)

A)1.9 × 10^-6 V
B)1.7 × 10^-6 V
C)2.2 × 10^-6 V
D)2.5 × 10^-6 V

Question 69

If the de Broglie wavelength of an electron is 2.4 ?m, what is the speed of the electron? $\left( m _ { \text {electron } } = 9.11 \times 10 ^ { - 31 } \mathrm {~kg} , \right.$ $\left. h = 6.626 \times 10 ^ { - 34 } \mathrm {~J} \cdot \mathrm { s } \right)$

A)3.0 × 10² m/s
B)2.5 × 10⁵ m/s
C)1.7 × 10³ m/s
D)8.3 × 10⁶ m/s

Question 70

If an electron has a wavelength of 0.123 nm, what is its kinetic energy, in electron-volts? This energy is not in the relativistic region. (m_electron = 9.11 × 10^-31 kg, 1 eV = 1.60 × 10^-19 J, h = 6.626 × 10^-34 J ∙ s)

A)19.8 eV
B)60.2 eV
C)80.4 eV
D)99.5 eV
E)124 eV

Question 71

A proton has a speed of 7.2 x $10 ^ { 4 }$ m/s. What is the energy of a photon that has the same wavelength as the de Broglie wavelength of this proton? (m_electron = 9.11 × 10^-31 kg, c = 3.00 × 10⁸ m/s, h = 6.626 × 10^-34 J ? s)

A)230 keV
B)150 keV
C)300 keV
D)370 keV
E)440 keV

Question 72

If an electron has the same de Broglie wavelength as the wavelength of a 390-nm photon in vacuum, what is the speed of the electron? (m_electron = 9.11 × 10^-31 kg, c = 3.0 × 10⁸ m/s, h = 6.626 × 10^-34 J ∙ s)

A)1900 m/s
B)2100 m/s
C)1700m/s
D)1500 m/s
E)540 m/s

Question 73

A person of mass 50 kg has a de Broglie wavelength of 4.4 × 10^-36 m while jogging. How fast is she running? (h = 6.626 × 10^-34 J ∙ s)

A)2.0 m/s
B)3.0 m/s
C)4.0 m/s
D)5.0 m/s

Question 74

Find the de Broglie wavelength of a 1.30-kg missile moving at $28.10 \mathrm {~m} / \mathrm { s }$ (h = 6.626 × 10^-34 J ? s)

A)1.81 × 10^-35 m
B)2.05 × 10^-35 m
C)2.28 × 10^-35 m
D)2.57 × 10^-35 m

Question 75

A crystal diffracts a beam of electrons, like a diffraction grating, as they hit it perpendicular to its surface. The crystal spacing is 0.18 nm, and the first maximum scattering occurs at 80° relative to the normal to the surface. (e = 1.60 × 10^-19 C, m_electron = 9.11 × 10^-13 kg, h = 6.626 × 10^-34 J ? s)
(a)What is the wavelength of the electrons?
(b)What potential difference accelerated the electrons if they started from rest?

Question 76

What would be the de Broglie wavelength for 1-g object moving at the earth's escape speed 25,000 mph (about 11 km/s)? (h = 6.626 × 10^-34 J ? s)

Question 77

An electron is moving with the speed of 1780 m/s. What is its de Broglie wavelength? (m_electron = 9.11 × 10^-31 kg, h = 6.626 × 10^-34 J ∙ s)

A)409 nm
B)302 nm
C)205 nm
D)420 nm
E)502 nm

Question 78

A proton that is moving freely has a wavelength of 0.600 pm. (m_proton = 1.67 × 10^-27 kg, e = 1.60 × 10^-19 C, h = 6.626 × 10^-34 J ? s)
(a)What is its momentum?
(b)What is its speed?
(c)What potential difference would it have been accelerated through, starting from rest, to reach this speed?

Question 79

Atoms in crystals are typically separated by distances of 0.10 nm. What kinetic energy must a nonrelativistic electron have, in electron-volts, in order to have a wavelength of 0.10 nm? (m_electron = 9.11 × 10^-31 kg, 1 eV = 1.60 × 10^-19 J, h = 6.626 × 10^-34 J ? s)

Question 80

The electrons in a beam are moving at 18 m/s. (m_electron = 9.11 × 10^-31 kg, h = 6.626 × 10^-34 J ? s)
(a)What is its de Broglie wavelength these electrons?
(b)If the electron beam falls normally on a diffraction grating, what would have to be the spacing between slits in the grating to give a first-order maximum at an angle of 30° with the normal to the grating?