# Quiz 38: Quantization

Physics & Astronomy

Q 1Q 1

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

Free

Multiple Choice

A

Q 2Q 2

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.

Free

Multiple Choice

A

Q 3Q 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.

Free

Multiple Choice

C, D

Free

True False

Q 5Q 5

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 × 10

^{8}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 eVFree

Multiple Choice

Q 6Q 6

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 × 10^{8}m/s, 1 eV = 1.60 × 10^{-19}J) A) 1.9 eV B) 2.0 eV C) 2.2 eV D) 2.3 eVFree

Multiple Choice

Q 7Q 7

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 × 10^{8}m/s, 1 eV = 1.60 × 10^{-19}J) A) 3.73 eV B) 3.13 eV C) 4.33 eV D) 4.92 eVFree

Multiple Choice

Q 8Q 8

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 × 10^{8}m/s, 1 eV = 1.60 × 10^{-19}J) A) 220 nm B) 150 nm C) 360 nm D) 1100 nmFree

Multiple Choice

Q 9Q 9

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 × 10^{8}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 nmFree

Multiple Choice

Q 10Q 10

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}JFree

Multiple Choice

Q 11Q 11

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 × 10^{14}_{ }Hz B) 2.7 × 10^{14}Hz C) 7.6 × 10^{14}_{ }Hz D) 8.5 × 10^{14}Hz E) 9.4 × 10^{14}HzFree

Multiple Choice

Q 12Q 12

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 × 10

^{8}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 nmFree

Multiple Choice

Q 13Q 13

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 × 10

^{8}m/s, h = 6.626 × 10^{-34}J ∙ s, e = - 1.60 × 10^{-19}C, 1 eV = 1.60 × 10^{-19}J)Free

Short Answer

Q 14Q 14

When a metal surface is illuminated with light of wavelength 437 nm, the stopping potential for photoelectrons is 1.67 V. (c = 3.00 × 10

^{8}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?Free

Essay

Q 15Q 15

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 × 10^{8}m/s) A) 1.0 × 10^{6}B) 1.4 × 10^{8}C) 6.2 × 10^{9}D) 3.9 × 10^{3}Free

Multiple Choice

Q 16Q 16

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}Free

Multiple Choice

Q 17Q 17

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 × 10^{8}m/s) A) 6.7 × 10^{15}B) 8.8 × 10^{15}C) 1.1 × 10^{16}D) 1.3 × 10^{16}Free

Multiple Choice

Q 18Q 18

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 × 10

^{8}m/s, h = 6.626 × 10^{-34}J ∙ s) A) 2.8 × 10^{18}B) 6.9 × 10^{19}C) 3.4 × 10^{19}D) 1.1 × 10^{17}E) 2.2 × 10^{17}Free

Multiple Choice

Q 19Q 19

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}mFree

Multiple Choice

Q 20Q 20

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.

Free

Multiple Choice

Q 21Q 21

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.

Free

Multiple Choice

Q 22Q 22

What is the frequency of the light emitted by atomic hydrogen with m = 8 and n = 12? (The Rydberg constant is R = 1.097 × 10

^{7}m^{-1},^{ }^{c }= 3.00 × 10^{8}m/s) A) 2.86 × 10^{13}Hz B) 1.43 × 10^{13}Hz C) 7.46 × 10^{13}Hz D) 8.82 × 10^{13}Hz E) 1.05 × 10^{13}HzFree

Multiple Choice

Q 23Q 23

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 nmFree

Multiple Choice

Q 24Q 24

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

Free

Multiple Choice

Q 25Q 25

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 × 10^{8}m/s, 1 eV = 1.60 × 10^{-19}J, the Rydberg constant is R = 1.097 × 10^{7}m^{-1}) A) 14 B) 16 C) 11 D) 21Free

Multiple Choice

Q 26Q 26

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 eVFree

Multiple Choice

Q 27Q 27

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 × 10^{8}m/s) A) 410 nm B) 93.8 nm C) 1090 nm D) 93.1 nmFree

Multiple Choice

Q 28Q 28

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 × 10^{14}Hz B) 0.865 × 10^{14}Hz C) 1.27 × 10^{14}Hz D) 4.05 × 10^{14}Hz E) 1.73 × 10^{14}HzFree

Multiple Choice

Q 29Q 29

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 × 10^{8}m/s) A) 2.43 μm B) 1.46 μm C) 1.94 μm D) 2.92 μmFree

Multiple Choice

Q 30Q 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 a

_{0}and the speed of an electron in that orbit is v_{0}. In the parallel universe (a) what would be the radius (in terms of a_{0}) of the first Bohr orbit for hydrogen? (b) what would be the speed (in terms of v_{0}) of an electron in the first Bohr orbit for hydrogen?Free

Short Answer

Q 31Q 31

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)Free

Short Answer

Q 32Q 32

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/sFree

Multiple Choice

Q 33Q 33

Electrons emerge from an electron gun with a speed of 2.0 × 10

^{6}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 nmFree

Multiple Choice

Q 34Q 34

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 × 10

^{4}m/s? (m_{proton}= 1.67 × 10^{-27}kg, c = 3.00 × 10^{8}m/s) A) 220 keV B) 150 keV C) 290 keV D) 360 keV E) 440 keVFree

Multiple Choice

Q 35Q 35

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 × 10^{8}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/sFree

Multiple Choice

Q 36Q 36

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 × 10^{8}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 keVFree

Multiple Choice

Q 37Q 37

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 mradFree

Multiple Choice

Q 38Q 38

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 × 10^{8}m/s, m_{e}_{l}= 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 nmFree

Multiple Choice

Q 39Q 39

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}mFree

Multiple Choice

Q 40Q 40

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 µVFree

Multiple Choice

Q 41Q 41

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 eVFree

Multiple Choice

Q 42Q 42

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 nmFree

Multiple Choice

Q 43Q 43

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) 41Free

Multiple Choice

Q 44Q 44

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 eVFree

Multiple Choice

Q 45Q 45

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 eVFree

Multiple Choice

Q 46Q 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 E

_{0}. 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 E_{0}.Free

Essay

Q 47Q 47

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 × 10

^{8}m/s, h = 6.626 × 10^{-34}J ∙ s, m_{el}= 9.11 × 10^{-}^{31}kg)Free

Short Answer

Q 48Q 48

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 × 10

^{8}m/s, h = 6.626 × 10^{-34}J ∙ 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?Free

Essay

Q 49Q 49

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 nmFree

Multiple Choice

Q 50Q 50

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) zeroFree

Multiple Choice

Q 51Q 51

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 µmFree

Multiple Choice

Q 52Q 52

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 nmFree

Multiple Choice

Q 53Q 53

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 × 10

^{8}m/s, h = 6.626 × 10^{-34}J ∙ s, m_{el}= 9.11 × 10^{-31}kg) A) 6.49 μm B) 5.45 μm C) 5.91 μm D) 7.07 μmFree

Multiple Choice

Q 54Q 54

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 × 10

^{8}m/s, h = 6.626 × 10^{-34}J ∙ s, m_{el}= 9.11 × 10^{-31}kg) A) 1.33 nm B) 1.12 nm C) 1.21 nm D) 1.45 nmFree

Multiple Choice

Q 55Q 55

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 MeVFree

Multiple Choice