Deck 38: Photons and Matter Waves

Question 1

In a photoelectric effect experiment no electrons are ejected if the frequency of the incident light is less than A/h, where h is the Planck constant and A is:

A) the maximum energy needed to eject the least energetic electron
B) the minimum energy needed to eject the least energetic electron
C) the maximum energy needed to eject the most energetic electron
D) the minimum energy needed to eject the most energetic electron
E) the intensity of the incident light

Answer 1

the minimum energy needed to eject the most energetic electron

Question 2

Which of the following electromagnetic radiations has photons with the greatest momentum?

A) blue light
B) yellow light
C) x rays
D) radio waves
E) microwaves

Answer 2

x rays

Question 3

A photon in light beam A has twice the energy of a photon in light beam B. The ratio p_A/p_B of their momenta is:

A) 1/2
B) 1/4
C) 1
D) 2
E) 4

Answer 3

2

Question 4

In a photoelectric effect experiment at a frequency above cut off, the number of electrons ejected is proportional to:

A) their kinetic energy
B) their potential energy
C) the work function
D) the frequency of the incident light
E) the number of photons that hit the sample

Question 5

Light beams A and B have the same intensity but the wavelength associated with beam A is longer than that associated with beam B. The photon flux (number crossing a unit area per unit time) is:

A) greater for A than for B
B) greater for B than for A
C) the same for A and B
D) greater for A than for B only if both have short wavelengths
E) greater for B than for A only if both have short wavelengths

Question 6

Rank following electromagnetic radiations according to the energies of their photons, from least to greatest.

A) 1, 2, 3, 4
B) 4, 2, 1, 3
C) 4, 1, 2, 3
D) 3, 2, 1, 4
E) 3, 1, 2, 4

Question 7

Which of the following electromagnetic radiations has photons with the greatest energy?

A) blue light
B) yellow light
C) x rays
D) radio waves
E) microwaves

Question 8

The wavelength of light beam B is twice the wavelength of light beam B. The energy of a photon in beam A is:

A) one-fourth the energy of a photon in beam B
B) half the energy of photon in beam B
C) equal to the energy of a photon in beam B
D) twice energy of a photon in beam B
E) four times the energy of a photon in beam B

Question 9

The main problem physicists had with understanding the photoelectric effect before Einstein explained it in terms of photons was:

A) the intensity of emitted electrons did not depend on the intensity of the source.
B) the maximum energy of the emitted electrons did not depend on the frequency of the source.
C) the maximum energy of the emitted electrons did not depend on the intensity of the source.
D) the cutoff frequency depended on the material used as a target.
E) the cutoff frequency did not depend on the material used as a target.

Question 10

In a photoelectric effect experiment the stopping potential is:

A) the energy required to remove an electron from the sample
B) the kinetic energy of the most energetic electron ejected
C) the potential energy of the most energetic electron ejected
D) the photon energy
E) the electric potential that causes the electron current to vanish

Question 11

In a photoelectric effect experiment at a frequency above cut off, the stopping potential is proportional to:

A) the energy of the least energetic electron before it is ejected
B) the energy of the least energetic electron after it is ejected
C) the energy of the most energetic electron before it is ejected
D) the energy of the most energetic electron after it is ejected
E) the electron potential energy at the surface of the sample

Question 12

The frequency of light beam A is twice that of light beam B. The ratio E_A/E_B of photon energies is:

A) 1/2
B) 1/4
C) 1
D) 2
E) 4

Question 13

In Compton scattering from stationary electrons the largest change in wavelength occurs when the photon is scattered through:

A) 0 $\degree$
B) 22.5 $\degree$
C) 45 $\degree$
D) 90 $\degree$
E) 180 $\degree$

Question 14

The quantization of energy, E = nhf, is not important for an ordinary pendulum because:

A) the formula applies only to mass-spring oscillators
B) the allowed energy levels are too closely spaced
C) the allowed energy levels are too widely spaced
D) the formula applies only to atoms
E) the value of h for a pendulum is too large

Question 15

The work function for a certain sample is 2.3 eV. The stopping potential for electrons ejected from the sample by 7.0 * 10¹⁴-Hz electromagnetic radiation is:

A) 0 V
B) 0.60 V
C) 2.3 V
D) 2.9 V
E) 5.2 V

Question 16

The concentration of photons in a uniform light beam with a wavelength of 500 nm is 1.7 *10¹³ m ^{- 3}. The intensity of the beam is:

A) 6.8 *10 ^{- 6} W/m²
B) 3.2 * 10² W/m²
C) 1.0 * 10³ W/m²
D) 2.0 *10³ W/m²
E) 4.0 * 10³ W/m²

Question 17

The diagram shows the graphs of the stopping potential as a function of the frequency of the incident light for photoelectric experiments performed on three different materials. Rank the materials according to the values of their work functions, from least to greatest.

A) 1, 2, 3
B) 3, 2, 1
C) 2, 3, 1
D) 2, 1, 3
E) 1, 3, 2

Question 18

The stopping potential for electrons ejected by 6.8 * 10¹⁴-Hz electromagnetic radiation incident on a certain sample is 1.8 V. The kinetic energy of the most energetic electrons ejected and the work function of the sample, respectively, are:

A) 1.8 eV, 2.8 eV
B) 1.8 eV, 1.0 eV
C) 1.8 eV, 4.6 eV
D) 2.8 eV, 1.0 eV
E) 1.0 eV, 4.6 eV

Question 19

The units of the Planck constant h are those of:

A) energy
B) power
C) momentum
D) angular momentum
E) frequency

Question 20

The intensity of a light beam with a wavelength of 500 nm is 2000 W/m². The photon flux is about:

A) 5* 10¹⁷ /m².s
B) 5 *10¹⁹ /m².s
C) 5 * 10²¹ /m².s
D) 5 * 10²³ /m².s
E) 5 *10²⁵ /m².s

Question 21

Consider the following three particles: Rank them according to the wavelengths of their matter waves, least to greatest.

A) 1, 2, 3
B) 3, 2, 1
C) 2, 3, 1
D) 1, 3, 2
E) 1, then 2 and 3 tied

Question 22

The frequency and wavelength of the matter wave associated with a 10-eV free electron are:

A) 1.5 * 10³⁴ Hz, 3.9 * 10^-10 m
B) 1.5*10³⁴ Hz, 1.3 *10^-34 m
C) 2.4 * 10¹⁵ Hz, 1.2 *10^-9 m
D) 2.4 * 10¹⁵ Hz, 3.9 *10^-10 m
E) 4.8* 10¹⁵ Hz, 1.9*10^-10 m

Question 23

Electromagnetic radiation with a wavelength of 3.5 * 10^-12 m is scattered from stationary electrons, and photons that have been scattered through 50 $\degree$ are detected. After a scattering event the magnitude of the photon's momentum is:

A) 0 kg.m/s
B) 8.7 *10^-23 kg.m/s
C) 1.5 * 10^-22 kg.m/s
D) 2.0 *10^-22 kg.m/s
E) 2.2 * 10^-22 kg.m/s

Question 24

In Compton scattering from stationary particles the maximum change in wavelength can be made smaller by using:

A) higher frequency radiation
B) lower frequency radiation
C) more massive particles
D) less massive particles
E) particles with greater charge

Question 25

The surface of the Sun is at a temperature of approximately 5800 K, and radiates a peak wavelength of 500 nm. According to the Planck radiation law, what is its emitted intensity per unit wavelength at the peak?

A) 8.4 W/cm²∙nm
B) 42 W/cm²∙nm
C) 84 W/cm²∙nm
D) 8.4 x 10³ W/cm²∙nm
E) 4.2 x 10⁷ W/cm²∙nm

Question 26

Electromagnetic radiation with a wavelength of 3.5 *10^-12 m is scattered from stationary electrons and photons that have been scattered through 50 $\degree$ are detected. An electron from which one of these photons was scattered receives an energy of:

A) 0 J
B) 1.1 * 10^-14 J
C) 1.9 *10^-14 J
D) 2.3 * 10^-14 J
E) 1.3 *10^-13 J

Question 27

Which of the following is NOT evidence for the wave nature of matter?

A) The photoelectric effect
B) The diffraction pattern obtained when electrons pass through a slit
C) Electron tunneling
D) The validity of the Heisenberg uncertainty principle
E) The interference pattern obtained when electrons pass through a two-slit system

Question 28

Separate Compton effect experiments are carried out using visible light and x rays. The scattered radiation is observed at the same scattering angle. For these experiments:

A) the x rays have the greater shift in wavelength and the greater change in photon energy
B) the two radiations have the same shift in wavelength and the x rays have the greater change in photon energy
C) the two radiations have the same shift in wavelength and the visible light has the greater change in photon energy
D) the two radiations have the same shift in wavelength and the same change in photon energy
E) the visible light has the greater shift in wavelength and the greater shift in photon energy

Question 29

Electromagnetic radiation with a wavelength of 5.7 * 10^-12 m is incident on stationary electrons. Radiation that has a wavelength of 6.6 * 10^-12 m is detected at a scattering angle of:

A) 10 $\degree$
B) 40 $\degree$
C) 50 $\degree$
D) 69 $\degree$
E) 111 $\degree$

Question 30

Evidence for the wave nature of matter is:

A) electron diffraction experiments of Davisson and Germer
B) Thompson's measurement of e/m
C) Young's double slit experiment
D) the Compton effect
E) Lenz's law

Question 31

Monoenergetic electrons are incident on a single slit barrier. If the energy of each incident electron is increased the central maximum of the diffraction pattern:

A) widens
B) narrows
C) stays the same width
D) widens for slow electrons and narrows for fast electrons
E) narrows for slow electrons and widens for fast electrons

Question 32

Of the following, Compton scattering from electrons is most easily observed for:

A) microwaves
B) infrared light
C) visible light
D) ultraviolet light
E) x rays

Question 33

In Compton scattering from stationary electrons the largest change in wavelength that can occur is:

A) 2.43 * 10^-15 m
B) 2.43 * 10^-12 m
C) 2.43 * 10^-9 m
D) dependent on the frequency of the incident light
E) dependent on the work function

Question 34

The main problem that physicists had in understanding blackbody radiation before Planck's work was:

A) Blackbody radiation came from objects that were not actually black.
B) The classically predicted frequency spectrum showed an infinitely large peak at low frequencies.
C) The classically predicted frequency spectrum showed an infinitely large peak at high frequencies.
D) The classically predicted frequency spectrum had a minimum intensity rather than a maximum as observed.
E) The classically predicted frequency spectrum had a maximum intensity that decreased with temperature, rather than increasing as observed.

Question 35

A free electron has a momentum of 5.0 * 10^-24 kg . m/s. Its wavelength, as given by its wave function, is:

A) 1.3 * 10^-8 m
B) 1.3 * 10^-10 m
C) 2.3 * 10^-11 m
D) 2.3 *10^-13 m
E) none of these

Question 36

Consider the following: I. A photoelectric process in which all emitted electrons have energy less than hf, where f is the frequency of the incident light.
II) A photoelectric process in which some emitted electrons have kinetic energy greater than hf.
III) Compton scattering from stationary electrons for which the emitted light has a frequency that is greater than that of the incident light.
IV) Compton scattering from stationary electrons for which the emitted light has a frequency that is less than that of the incident light.
The only possible processes are:

A) I
B) III
C) I and III
D) I and IV
E) II and IV

Question 37

Of the following which is the best evidence for the wave nature of matter?

A) The photoelectric effect
B) The Compton effect
C) The spectral radiancy of cavity radiation
D) The relationship between momentum and energy for an electron
E) The reflection of electrons by crystals

Question 38

What is the temperature of a burner on an electric stove when its glow is barely visible, at a wavelength of 700 nm? Assume the burner radiates as an ideal blackbody and that 700 nm represents the peak of its emission spectrum.

A) 41 K
B) 240 K
C) 410 K
D) 2400 K
E) 4100 K

Question 39

In Compton scattering from stationary electrons the frequency of the emitted light is independent of:

A) the frequency of the incident light
B) the recoil speed of the electron
C) the scattering angle
D) the electron recoil energy
E) none of the above

Question 40

Consider the following three particles: Rank them according to the wavelengths of their waves, least to greatest.

A) 1, 2, 3
B) 3, 2, 1
C) 2, 3, 1
D) 1, 3, 2
E) 1, then 2 and 3 tied

Question 41

The uncertainty in position of an electron in a certain state is 5 * 10^-10 m. The uncertainty in its momentum could be

A) 5.0 * 10^-24 kg.m/s
B) 4.0 *10^-24 kg.m/s
C) 3.0 *10^-24 kg.m/s
D) any of the above
E) none of the above

Question 42

A free electron in motion along the x axis has a localized wave function. The uncertainty in its momentum is decreased if:

A) the wave function is made more narrow
B) the wave function is made less narrow
C) the wave function remains the same but the energy of the electron is increased
D) the wave function remains the same but the energy of the electron is decreased
E) none of the above

Question 43

An electron with energy E is incident upon a potential energy barrier of height E_pot < E and thickness L. The reflection coefficient R:

A) is always equal to zero
B) is always equal to 1
C) does not depend on E - E_pot
D) is, in general, not equal to zero
E) is equal to T + 1 where T is the transmission coefficient

Question 44

The probability that a particle is in a given small region of space is proportional to:

A) its energy
B) its momentum
C) the magnitude of its wave function
D) the wavelength of its wave function
E) the square of the magnitude of its wave function

Question 45

Identical particles, each with energy E, are incident on the following four potential energy barriers: Rank the barriers in terms of the probability that the particles tunnel through them, from least probability to greatest probability.

A) 1, 2, 3, 4
B) 4, 3, 2, 1
C) 1 and 2 tied, then 3, then4
D) 1, then 2 and 3 tied, then 4
E) 3, 2, 1, 4

Question 46

The significance of $\mid$$\Psi$$\mid$ ² is:

A) probability
B) energy
C) probability density
D) energy density
E) wavelength

Question 47

An electron with energy E is incident on a potential energy barrier of height E_pot and thickness L. The probability of tunneling increases if:

A) E decreases without any other changes
B) E_pot increases without any other changes
C) L decreases without any other changes
D) E and E_pot increase by the same amount
E) E and E_pot decrease by the same amount

Question 48

An electron with energy E is incident upon a potential energy barrier of height E_pot < E and thickness L. If the reflection coefficient R = 0.05,

A) the electron has a 0.05% chance of being reflected
B) the electron has a 5% chance of being reflected
C) the electron has a 95% chance of being reflected
D) the electron will be partially reflected and partially transmitted
E) the electron has no chance of being reflected

Question 49

A free electron and a free proton have the same momentum. This means that, compared to the matter wave associated with the proton, the matter wave associated with the electron has:

A) a shorter wavelength and a greater frequency
B) a longer wavelength and a greater frequency
C) the same wavelength and the same frequency
D) the same wavelength and a greater frequency
E) the same wavelength and a smaller frequency

Question 50

The reflection coefficient R for a certain barrier tunneling problem is 0.80. The corresponding transmission coefficient T is:

A) 0.80
B) 0.60
C) 0.50
D) 0.20
E) 0

Question 51

A free electron in motion along the x axis has a localized wave function. If it enters a region of space where its potential energy increases,

A) its total energy will decrease.
B) its momentum will increase.
C) its wave number will increase.
D) its wavelength will increase.
E) its kinetic energy will increase.

Question 52

A free electron and a free proton have the same speed. This means that, compared to the matter wave associated with the proton, the matter wave associated with the electron has:

A) a shorter wavelength and a greater frequency
B) a longer wavelength and a greater frequency
C) a shorter wavelength and a smaller frequency
D) the same wavelength and a greater frequency
E) a longer wavelength and a smaller frequency

Question 53

In order to tunnel through a potential barrier a particle must:

A) have energy greater than the barrier height
B) have spin
C) be massive
D) have a wavelength longer than the barrier width
E) none of the above

Question 54

A non-relativistic free electron has kinetic energy K. If its wavelength doubles, its kinetic energy is:

A) 4 K
B) 2 K
C) K
D) K/2
E) K/4

Question 55

Maxwell's equations are to electric and magnetic fields as __________ equation is to the wave function of the particle.

A) Einstein's
B) Fermi's
C) Newton's
D) Schrödinger's
E) Bohr's

Question 56

A free electron and a free proton have the same kinetic energy. This means that, compared to the matter wave associated with the proton, the matter wave associated with the electron has:

A) a shorter wavelength and a greater frequency
B) a longer wavelength and a greater frequency
C) a shorter wavelength and the same frequency
D) a longer wavelength and the same frequency
E) a shorter wavelength and a smaller frequency

Question 57

An electron with energy E is incident upon a potential energy barrier of height E_pot > E and thickness L. The transmission coefficient T:

A) is zero
B) decreases exponentially with L
C) is proportional to 1/L
D) is proportional to 1/L²
E) is non-zero and independent of L