Deck 38: Quantization

Question 1

In a photoelectric effect experiment, electrons emerge from a copper surface with a maximum kinetic energy of 1.10 eV when light shines on the surface. The work function of copper is 4.65 eV. Which one of the following values is closest to the wavelength of the light? (h = 6.626 × 10^-34 J ∙ s, c = 3.00 × 10⁸ m/s, 1 eV = 1.60 × 10^-19 J)

A) 220 nm
B) 150 nm
C) 360 nm
D) 1100 nm

Answer 1

220 nm

Question 2

The smallest kinetic energy that an electron in a box (an infinite well) can have is zero.

Answer 2

False

Question 3

A nonrelativistic electron and a nonrelativistic proton have the same de Broglie wavelength. Which of the following statements about these particles are accurate? (There may be more than one correct choice.)

A) Both particles have the same speed.
B) Both particles have the same kinetic energy.
C) Both particles have the same momentum.
D) The electron has more kinetic energy than the proton.
E) The electron has more momentum than the proton.

Answer 3

Both particles have the same momentum.
The electron has more kinetic energy than the proton.

Question 4

When a certain metal is illuminated by light, photoelectrons are observed provided that the wavelength of the light is less than 669 nm. Which one of the following values is closest to the work function of this metal? (h = 6.626 × 10^-34 J ∙ s, c = 3.00 × 10⁸ m/s, 1 eV = 1.60 × 10^-19 J)

A) 1.9 eV
B) 2.0 eV
C) 2.2 eV
D) 2.3 eV

Question 5

Gamma rays are photons with very high energy. How many visible-light photons with a wavelength of 500 nm would you need to match the energy of a gamma-ray photon with energy
4.1 × 10^-13 J? (h = 6.626 × 10^-34 J ∙ s, c = 3.00 × 10⁸ m/s)

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

Question 6

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 × 10³²
B) 2.9 × 10²⁴
C) 6.3 × 10¹²
D) 1.4 × 10¹⁵

Question 7

A beam of red light and a beam of violet light each deliver the same power on a surface. For which beam is the number of photons hitting the surface per second the greatest?

A) the red beam
B) the violet beam
C) It is the same for both beams.

Question 8

Upon being struck by 240-nm photons, a metal ejects electrons with a maximum kinetic energy of What is the work function of this metal? (h = 6.626 × 10^-34 J ∙ s, c = 3.00 × 10⁸ m/s,
1 eV = 1.60 × 10^-19 J)

A) 3.73 eV
B) 3.13 eV
C) 4.33 eV
D) 4.92 eV

Question 9

A stopping potential of 0.50 V is required when a phototube is illuminated with monochromatic light of wavelength 590 nm. Monochromatic light of a different wavelength is now shown on the tube, and the stopping potential is measured to be 2.30 V. What is the wavelength of this new light? (c = 3.00 × 10⁸ m/s, e = - 1.60 × 10^-19 C, h = 6.626 × 10^-34 J ∙ s, 1 eV = 1.60 × 10^-19 J)

A) 320 nm
B) 300 nm
C) 340 nm
D) 360 nm
E) 410 nm

Question 10

A laser emits light of wavelength 463 nm during a brief pulse that lasts for 25 ms and has a total energy of 1.2 J. How many photons are emitted in that single pulse? (c = 3.00 × 10⁸ m/s, h = 6.626 × 10^-34 J ∙ s)

A) 2.8 × 10¹⁸
B) 6.9 × 10¹⁹
C) 3.4 × 10¹⁹
D) 1.1 × 10¹⁷
E) 2.2 × 10¹⁷

Question 11

The Bohr radius of the hydrogen atom is 0.529 × 10^-10 m. What is the radius of the n = 2 state?

A) 1.06 × 10^-10 m
B) 2.12 × 10^-10 m
C) 0.265 × 10^-10 m
D) 0.529 × 10^-10 m
E) 4.23 × 10^-10 m

Question 12

When a metal surface is illuminated with light of wavelength 437 nm, the stopping potential for photoelectrons is 1.67 V. (c = 3.00 × 10⁸ m/s, h = 6.626 × 10^-34 J ∙ s, e = - 1.60 × 10^-19 C, 1 eV = 1.60 × 10^-19 J, m_el = 9.11 × 10^-31 kg)
(a) What is the work function of the metal, in eV?
(b) What is the maximum speed of the ejected electrons?

Question 13

Light of wavelength 400 nm falls on a metal surface having a work function 1.70 eV. What is the maximum kinetic energy of the photoelectrons emitted from the metal? (c = 3.00 × 10⁸ m/s, h = 6.626 × 10^-34 J ∙ s = 4.141 × 10^-15 ev ∙ s, 1 eV = 1.60 × 10^-19 J)

A) 4.52 eV
B) 3.11 eV
C) 1.41 eV
D) 2.82 eV
E) 1.70 eV

Question 14

A metal having a work function of 2.4 eV is illuminated with monochromatic light whose photon energy is 4.0 eV. What is the maximum kinetic energy of the photoelectrons produced by this light? (h = 6.626 × 10^-34 J ∙ s, 1 eV = 1.60 × 10^-19 J)

A) 2.6 × 10^-19 J
B) 3.8 × 10^-19 J
C) 4.7 × 10^-19 J
D) 5.5 × 10^-19 J
E) 6.4 × 10^-19 J

Question 15

A metal surface has a work function of 1.50 eV. Calculate the maximum kinetic energy, in eV, of electrons ejected from this surface by electromagnetic radiation of wavelength 311 nm. (c = 3.00 × 10⁸ m/s, h = 6.626 × 10^-34 J ∙ s, e = - 1.60 × 10^-19 C, 1 eV = 1.60 × 10^-19 J)

Question 16

A light beam from a 2.1-mW He-Ne laser has a wavelength of 633 nm. How many photons does the laser emit in one second? (h = 6.626 × 10^-34 J ∙ s, c = 3.00 × 10⁸ m/s)

A) 6.7 × 10¹⁵
B) 8.8 × 10¹⁵
C) 1.1 × 10¹⁶
D) 1.3 × 10¹⁶

Question 17

A metal having a work function of 2.5 eV is illuminated with white light that has a continuous wavelength band from 400 nm to 700 nm. For which one of the following ranges of the wavelength band in this white light are photoelectrons NOT produced? (h = 6.626 × 10^-34 J ∙ s, c = 3.00 × 10⁸ m/s, 1 eV = 1.60 × 10^-19 J)

A) 500 nm to 700 nm
B) 400 nm to 560 nm
C) 500 nm to 560 nm
D) 400 nm to 500 nm
E) 560 nm to 700 nm

Question 18

The energy of the ground state in the Bohr model of the hydrogen atom is -13.6 eV. The energy of the n = 2 state of hydrogen in this model is closest to

A) -3.4 eV.
B) -6.8 eV.
C) -1.7 eV.
D) -13.6 eV.
E) -4.5 eV.

Question 19

A metal having a work function of 2.8 eV is illuminated with monochromatic light whose photon energy is 3.9 eV. What is the threshold frequency for photoelectron production? (h = 6.626 × 10^-34 J ∙ s, 1 eV = 1.60 × 10^-19 J)

A) 6.8 × 10¹⁴ Hz
B) 2.7 × 10¹⁴ Hz
C) 7.6 × 10¹⁴ Hz
D) 8.5 × 10¹⁴ Hz
E) 9.4 × 10¹⁴ Hz

Question 20

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

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

Question 21

A hydrogen atom initially in the n = 6 state decays to the n = 2 state. The emitted photon is detected in a photographic plate. What is the wavelength of the detected photon? The lowest level energy state of hydrogen is -13.6 eV. (h = 6.626 × 10^-34 J ∙ s, 1 eV = 1.60 × 10^-19 J, c = 3.00 × 10⁸ m/s)

A) 410 nm
B) 93.8 nm
C) 1090 nm
D) 93.1 nm

Question 22

Calculate the kinetic energy (in eV) of a nonrelativistic neutron that has a de Broglie wavelength of 9.9 × 10^-12 m. (h = 6.626 × 10^-34 J ∙ s, m_neutron = 1.675 × 10^-27 kg, 1 eV = 1.60 10^-19 J)

Question 23

Light shines through atomic hydrogen gas. It is seen that the gas absorbs light readily at a wavelength of 91.63 nm. What is the value of n of the level to which the hydrogen is being excited by the absorption of light of this wavelength? Assume that the most of the atoms in the gas are in the lowest level. (h = 6.626 × 10^-34 J ∙ s, c = 3.00 × 10⁸ m/s, 1 eV = 1.60 × 10^-19 J, the Rydberg constant is R = 1.097 × 10⁷ m^-1)

A) 14
B) 16
C) 11
D) 21

Question 24

What is the frequency of the light emitted by atomic hydrogen with m = 8 and n = 12? (The Rydberg constant is R = 1.097 × 10⁷ m^-1, ^c = 3.00 × 10⁸ m/s)

A) 2.86 × 10¹³ Hz
B) 1.43 × 10¹³ Hz
C) 7.46 × 10¹³ Hz
D) 8.82 × 10¹³ Hz
E) 1.05 × 10¹³ Hz

Question 25

Light of wavelength 105 nm falls on a metal surface for which the work function is 5.00 eV. What is the minimum de Broglie wavelength of the photoelectrons emitted from this metal? (h = 6.626 × 10^-34 J ∙ s = 4.14 × 10^-15 eV ∙ s, c = 3.00 × 10⁸ m/s, m_el = 9.11 × 10^-31 kg, 1 eV = 1.60 × 10^-19 J)

A) 0.24 nm
B) 0.33 nm
C) 0.47 nm
D) 0.66 nm
E) 0.94 nm

Question 26

Electrons emerge from an electron gun with a speed of 2.0 × 10⁶ m/s and then pass through a pair of thin parallel slits. Interference fringes with a spacing of 2.7 mm are detected on a screen far from the double slit and fairly close to the center of the pattern. What would the fringe spacing be if the electrons were replaced by neutrons with the same speed? (m_el = 9.11 × 10^-31 kg, m_neutron = 1.67 × 10^-27 kg)

A) 1.5 µm
B) 4.9 µm
C) 0.93 nm
D) 1.1 µm
E) 1.5 nm

Question 27

The energy of the ground state in the Bohr model of the hydrogen atom is -13.6 eV. In a transition from the n = 2 state to the n = 4 state, a photon of energy

A) 3.40 eV is emitted.
B) 3.40 eV is absorbed.
C) 2.55 eV is emitted.
D) 2.55 eV is absorbed.
E) 0.85 eV is absorbed.

Question 28

A hydrogen atom is in its n = 2 excited state when its electron absorbs a photon of energy 8.5 eV. What is the energy of the resulting free electron? The lowest level energy state of hydrogen is -13.6 eV. (h = 6.626 × 10^-34 J ∙ s, 1 eV = 1.60 × 10^-19 J)

A) 5.1 eV
B) 6.6 eV
C) 6.9 eV
D) 7.6 eV

Question 29

Light excites atomic hydrogen from its lowest level to the n = 4 level. What is the energy of the light? The energy of the lowest level is -13.6 eV.

A) 12.8 eV
B) 3.40 eV
C) 0.850 eV
D) 26.4 eV

Question 30

Suppose that in a parallel universe, the proton and electron were identical to their counterparts in our own universe EXCEPT that the electron had twice as much charge as our electron. In our present universe, the radius of the first Bohr orbit for hydrogen is a₀ and the speed of an electron in that orbit is v₀. In the parallel universe
(a) what would be the radius (in terms of a₀) of the first Bohr orbit for hydrogen?
(b) what would be the speed (in terms of v₀) of an electron in the first Bohr orbit for hydrogen?

Question 31

A nonrelativistic electron has a kinetic energy of 5.4 eV. What is the energy of a photon whose wavelength is the same as the de Broglie wavelength of the electron? (m_el = 9.11 × 10^-31 kg, c = 3.00 × 10⁸ m/s, 1 eV = 1.60 × 10^-19 J)

A) 2.4 keV
B) 2.2 keV
C) 2.0 keV
D) 2.5 keV
E) 2.7 keV

Question 32

What is the energy of a photon that has a wavelength equal to the de Broglie wavelength of a proton having a speed of 7.1 × 10⁴ m/s? (m_proton = 1.67 × 10^-27 kg, c = 3.00 × 10⁸ m/s)

A) 220 keV
B) 150 keV
C) 290 keV
D) 360 keV
E) 440 keV

Question 33

How fast must a nonrelativistic electron move so its de Broglie wavelength is the same as the wavelength of a 3.4-eV photon? (m_el = 9.11 × 10^-31 kg, c = 3.00 × 10⁸ m/s, 1 eV = 1.60 × 10^-19 J)

A) 2000 m/s
B) 1900 m/s
C) 1700 m/s
D) 1600 m/s
E) 1400 m/s

Question 34

In a double slit experiment, a beam of electrons strikes a pair of slits. The slits are 15 μm apart, and the first interference maximum lies at an angle of 0.50 µrad from the center of the interference pattern. What is the momentum of the incoming electrons? (h = 6.626 × 10^-34 J ∙ s, m_el = 9.11 × 10^-31 kg)

A) 4.4 × 10^-23 kg ∙ m/s
B) 2.2 × 10^-23 kg ∙ m/s
C) 1.1 × 10^-23 kg ∙ m/s
D) 6.6 × 10^-23 kg ∙ m/s
E) 8.8 × 10^-23 kg ∙ m/s

Question 35

A hydrogen atom is excited to the n = 10 stated. It then decays to the n = 4 state by emitting a photon which is detected in a photographic plate. What is the frequency of the detected photon? The lowest level energy state of hydrogen is -13.6 eV. (h = 6.626 × 10^-34 J ∙ s, 1 eV = 1.60 × 10^-19 J)

A) 3.46 × 10¹⁴ Hz
B) 0.865 × 10¹⁴ Hz
C) 1.27 × 10¹⁴ Hz
D) 4.05 × 10¹⁴ Hz
E) 1.73 × 10¹⁴ Hz

Question 36

A gas of helium atoms (each of mass 6.65 × 10^-27 kg) are at room temperature of 20.0°C. What is the de Broglie wavelength of the helium atoms that are moving at the root-mean-square speed? (h = 6.626 × 10^-34 J ∙ s, the Boltzmann constant is 1.38 × 10^-23 J/K)

A) 5.22 × 10^-11 m
B) 7.38 × 10^-11 m
C) 1.04 × 10^-10 m
D) 2.82 × 10^-10 m
E) 3.99 × 10^-10 m

Question 37

What is the orbital radius of the n = 3 excited state in the Bohr model of the hydrogen atom? The ground-state radius of the hydrogen atom is 0.529 × 10^-10 m.

A) 0.476 nm
B) 0.159 nm
C) 0.381 nm
D) 0.548 nm

Question 38

A hydrogen atom makes a downward transition from the n = 20 state to the n = 5 state. Find the wavelength of the emitted photon. The lowest level energy state of hydrogen is -13.6 eV.
(h = 6.626 × 10^-34 J ∙ s, 1 eV = 1.60 × 10^-19 J, c = 3.00 × 10⁸ m/s)

A) 2.43 μm
B) 1.46 μm
C) 1.94 μm
D) 2.92 μm

Question 39

A nonrelativistic electron is accelerated from rest through a potential difference. After acceleration the electron has a de Broglie wavelength of 880 nm. What is the potential difference though which this electron was accelerated? (h = 6.626 × 10^-34 J ∙ s, e = - 1.60 × 10^-19 C, m_el = 9.11 × 10^-31 kg)

A) 1.9 µV
B) 1.7 µV
C) 2.2 µV
D) 2.5 µV

Question 40

A single slit is illuminated at normal incidence with a parallel beam of light having a wavelength of The entire central band of the diffraction pattern is observed at ±90°. The illumination is now replaced by a nonrelativistic beam of electrons, each having a kinetic energy of 980 eV. When this beam hits the slit at normal incidence, at what angle will the first minimum of the electron diffraction pattern occur? (h = 6.626 × 10^-34 J ∙ s, m_el = 9.11 × 10^-31 kg, 1 eV = 1.60 × 10^-19 J)

A) 0.095 mrad
B) 0.071 mrad
C) 0.046 mrad
D) 0.12 mrad
E) 0.14 mrad

Question 41

An electron is in the ground state of an infinite well (a box) where its energy is 5.00 eV. In the next higher level, what would its energy be? (1 eV = 1.60 × 10^-19 J)

A) 1.25 eV
B) 2.50 eV
C) 10.0 eV
D) 15.0 eV
E) 20.0 eV

Question 42

A 10.0-g bouncy ball is confined in a 8.3-cm-long box (an infinite well). If we model the ball as a point particle, what is the minimum kinetic energy of the ball? (h = 6.626 × 10^-34 J ∙ s)

A) 8.0 × 10^-64 J
B) 3.2 × 10^-46 J
C) 1.3 × 10^-20 J
D) zero

Question 43

An electron is bound in an infinite well (a box) of width 0.10 nm. If the electron is initially in the n = 8 state and falls to the n = 7 state, find the wavelength of the emitted photon. (c = 3.00 × 10⁸ m/s, h = 6.626 × 10^-34 J ∙ s, m_el = 9.11 × 10^-31 kg)

Question 44

An electron is in an infinite square well (a box) that is 8.9 nm wide. What is the ground state energy of the electron? (h = 6.626 × 10^-34 J ∙ s, m_el = 9.11 × 10^-31 kg, 1 eV = 1.60 × 10^-19)

A) 0.0048 eV
B) 0.0057 eV
C) 0.0066 eV
D) 0.0076 eV
E) 0.0085 eV

Question 45

You want to confine an electron in a box (an infinite well) so that its ground state energy is 5.0 × 10^-18 J. What should be the length of the box? (h = 6.626 × 10^-34 J ∙ s, m_el = 9.11 × 10^-31 kg)

A) 0.11 nm
B) 0.22 nm
C) 0.15 nm
D) 0.18 nm

Question 46

The lowest energy level of a particle confined to a one-dimensional region of space (a box, or infinite well) with fixed length L is E₀. If an identical particle is confined to a similar region with fixed length L/6, what is the energy of the lowest energy level that the particles have in common? Express your answer in terms of E₀.

Question 47

An electron is bound in an infinite square-well potential (a box) on the x-axis. The width of the well is L and the well extends from x = 0.00 nm to In its present state, the normalized wave function of the electron is given by: ψ(x) =

Sin (2πx/L). What is the energy of the electron in this state?(h = 6.626 × 10^-34 J ∙ s, m_el = 9.11 × 10^-31 kg, 1 eV = 1.60 × 10^-19)

A) 0.10 eV
B) 0.052 eV
C) 0.13 eV
D) 0.078 eV
E) 0.026 eV

Question 48

You want to have an electron in an energy level where its speed is no more than 66 m/s. What is the length of the smallest box (an infinite well) in which you can do this? (h = 6.626 × 10^-34 J ∙ s,
M_el = 9.11 × 10^-31 kg)

A) 5.5 µm
B) 11 µm
C) 2.8 µm
D) 1.4 µm

Question 49

An electron in an infinite potential well (a box) makes a transition from the n = 3 level to the ground state and in so doing emits a photon of wavelength 20.9 nm. (c = 3.00 × 10⁸ m/s, h = 6.626 × 10^-34J ∙ s, m_el = 9.11 × 10^-31 kg)
(a) What is the width of this well?
(b) What wavelength photon would be required to excite the electron from its original level to the next higher one?

Question 50

A particle confined in a rigid one-dimensional box (an infinite well) of length 17.0 fm has an energy level E_n = 24.0 MeV and an adjacent energy level E_n+1 = 37.5 MeV. What is the value of the ground state energy? (1 eV = 1.60 × 10^-19 J)

A) 1.50 MeV
B) 13.5 MeV
C) 0.500 MeV
D) 4.50 MeV

Question 51

An electron is trapped in an infinite square well (a box) of width 6.88 nm. Find the wavelength of photons emitted when the electron drops from the n = 5 state to the n = 1 state in this system. (c = 3.00 × 10⁸ m/s, h = 6.626 × 10^-34J ∙ s, m_el = 9.11 × 10^-31 kg)

A) 6.49 μm
B) 5.45 μm
C) 5.91 μm
D) 7.07 μm

Question 52

One fairly crude method of determining the size of a molecule is to treat the molecule as an infinite square well (a box) with an electron trapped inside, and to measure the wavelengths of emitted photons. If the photon emitted during the n = 2 to n = 1 transition has wavelength 1940 nm, what is the width of the molecule? (c = 3.00 × 10⁸ m/s, h = 6.626 × 10^-34J ∙ s, m_el = 9.11 × 10^-31 kg)

A) 1.33 nm
B) 1.12 nm
C) 1.21 nm
D) 1.45 nm

Question 53

An electron is in an infinite square well (a box) that is 2.0 nm wide. The electron makes a transition from the n = 8 to the n = 7 state, what is the wavelength of the emitted photon?(h = 6.626 × 10^-34 J ∙ s, m_el = 9.11 × 10^-31 kg, 1 eV = 1.60 × 10^-19)

A) 880 nm
B) 750 nm
C) 610 nm
D) 1000 nm
E) 1100 nm

Question 54

An electron is confined in a one-dimensional box (an infinite well). Two adjacent allowed energies of the electron are 1.068 × 10^-18 J and 1.352 × 10^-18 J. What is the length of the box? (h = 6.626 × 10^-34 J ∙ s, m_el = 9.11 × 10^-31 kg)

A) 1.9 nm
B) 0.93 nm
C) 1.1 nm
D) 2.3 nm

Question 55

An electron is in an infinite square well that is 2.6 nm wide. What is the smallest value of the state quantum number n for which the energy level exceeds 100 eV? (h = 6.626 × 10^-34 J ∙ s, m_el = 9.11 × 10^-31 kg, 1 eV = 1.60 × 10^-19)

A) 43
B) 44
C) 45
D) 42
E) 41