Deck 28: Quantum Physics

Question 1

What is the energy of a photon that has the same wavelength as an electron with kinetic energy 1.60 × 10⁻¹⁵ J?

A) 10.0 keV
B) 101 keV
C) 55.3 keV
D) 5.53 keV
E) 6.77 keV

Answer 1

101 keV

Question 2

In the Bohr model of the hydrogen atom, how is the circumference C of the ground-state orbit of the electron related to the de Broglie wavelength λ of the electron?

A) λ = C
B) λ = C/π
C) λ = C/2π
D) λ = πC
E) λ = 2πC

Answer 2

λ = C

Question 3

What is the de Broglie wavelength of an electron in the n = 2 state of the hydrogen atom in the Bohr model?

A) 5.20 × 10⁻¹¹ m
B) 1.66 × 10⁻¹⁰ m
C) 3.32 × 10⁻¹⁰ m
D) 6.65 × 10⁻¹⁰ m
E) 1.33 × 10⁻⁹ m

Answer 3

6.65 × 10⁻¹⁰ m

Question 4

A particle with mass and nonzero kinetic energy will

A) always have the same wavelength as a photon with the same kinetic energy.
B) always have a greater wavelength than a photon with the same kinetic energy.
C) always have a shorter wavelength than a photon with the same kinetic energy.
D) sometimes have a greater wavelength than a photon with the same kinetic energy.
E) sometimes have a shorter wavelength than a photon with the same kinetic energy.

Question 5

What is the de Broglie wavelength of an electron with kinetic energy 1.60 × 10⁻¹⁵ J?

A) 61.2 nm
B) 612 nm
C) 1.20 fm
D) 13.7 pm
E) 12.3 pm

Question 6

If the momentum of a particle is doubled, what happens to its de Broglie wavelength?

A) It doubles.
B) It halves.
C) It slightly more than doubles.
D) It becomes slightly less than half.
E) It decreases by a factor of 2^−1/2.

Question 7

In the ground state of the hydrogen atom, the probability of finding the electron is maximum at what radius? Express your answer in terms of the Bohr radius a₀.

A) 0.707 a₀
B) a₀
C) 1.41 a₀
D) 2 a₀
E) 1.73 a₀

Question 8

What is the de Broglie wavelength of a 0.40 kg object moving at 25 m/s?

A) 0.40 kg objects don't have wavelengths
B) 10 m
C) 0.10 m
D) 6.6 × 10⁻³⁵ m
E) 0.53 × 10⁻¹⁰ m

Question 9

The probability of finding a particle with wave function ψ in an interval ∆x is given by

A) ψ.
B) ψ ∆x.
C) |ψ| (∆x)².
D) |ψ²| ∆x.
E) |ψ²| (∆x)².

Question 10

Which of the following demonstrates the particle properties of light?

A) diffraction
B) interference
C) photoelectric effect
D) refraction

Question 11

Which of the following demonstrates the wave properties of light?

A) photoelectric effect
B) Compton effect
C) diffraction
D) pair production

Question 12

An electron and a neutron have the same de Broglie wavelength. Which statement is true?

A) The electron and neutron have the same kinetic energy, but the electron has the higher speed.
B) The neutron has more kinetic energy but the two have the same speed.
C) The electron has more kinetic energy and a higher speed.
D) The electron has less kinetic energy and a lower speed.
E) The electron has less kinetic energy but a higher speed.

Question 13

A bullet is fired from a rifle. The end of the barrel is a circular aperture. Is diffraction a measurable effect?

A) Yes.
B) No, because only subatomic particles have de Broglie wavelengths.
C) No, because a circular aperture never causes diffraction.
D) No, because the de Broglie wavelength of the bullet is too large relative to the aperture.
E) No, because the de Broglie wavelength of the bullet is too small relative to the aperture.

Question 14

If an electron is accelerated from rest through a potential difference of 100 V, what is its de Broglie wavelength?

A) 2.55 × 10⁻⁹ m
B) 1.23 × 10⁻¹⁰ m
C) 0.529 × 10⁻¹⁰ m
D) 8.67 × 10⁻⁹ m
E) 1.20 × 10⁻¹⁵ m

Question 15

What accelerating potential in an electron microscope would give electrons a wavelength 1.00 × 10⁻¹⁰ m?

A) 37.5 V
B) 75.0 V
C) 150 V
D) 300 V

Question 16

What is the de Broglie wavelength of a neutron with kinetic energy 44.0 keV? The mass of a neutron is 939.6 MeV/c².

A) 56.4 pm
B) 0.136 pm
C) 0.166 pm
D) 2.83 pm
E) 5.11 pm

Question 17

In the Bohr model of hydrogen, what is the ratio of the de Broglie wavelength of the electron in the n = 4 state to the wavelength in the n = 1 state?

A) 1
B) 2
C) 4
D) 16
E) 0.25

Question 18

In the Bohr model of the hydrogen atom, how is the circumference C_n of the n^th orbit of the electron related to the de Broglie wavelength λ_n of the electron?

A) λ_n = C_n
B) λ_n = C_n/n
C) λ_n = nC_n
D) λ_n = C_n/n²
E) λ_n = C_n/2π

Question 19

Who first observed wavelike interference and diffraction effects in the scattering of electrons by a crystalline target?

A) J. J. Thompson
B) Louis de Broglie
C) Niels Bohr
D) Einstein and Planck
E) Davisson and Germer

Question 20

Considering only the limitations of diffraction, what is the smallest structure resolvable using a 12 keV electron microscope?

A) 3.4 × 10⁻¹⁹ m
B) 1.1 × 10⁻¹¹ m
C) 1.8 × 10⁻⁴ m
D) 10 cm

Question 21

How do the energy-level spacings for a particle in a box change when the box is made longer?

A) decrease
B) stay the same
C) increase
D) not enough information

Question 22

Quantum-mechanical wave functions are solutions of what equation?

A) the Heisenberg equation
B) the Bohr equation
C) the Born equation
D) the Schrödinger equation
E) the de Broglie equation

Question 23

Which one of the following is true?

A) The principal quantum number of the electron in a hydrogen atom does not affect its energy.
B) The orbital angular momentum quantum number of an electron state is always less than the principal quantum number.
C) The electron spin quantum number can take on any one of four different values.
D) The principal quantum number of an electron in the ground state is zero.

Question 24

For a particle in a one-dimensional box, what happens to the ground-state energy if the width of the box is halved?

A) nothing, it stays the same
B) it doubles
C) it halves
D) it quadruples
E) it quarters

Question 25

Using the energy-time version of the uncertainty principle, estimate the uncertainty in the energy of a state with lifetime of 10⁻⁹ s.

A) 10⁻² eV
B) 10⁻⁷ eV
C) 10⁻¹² eV
D) 10⁻¹⁵ eV
E) 10⁻¹⁸ eV

Question 26

The uncertainty principle was formulated by

A) Albert Einstein.
B) Niels Bohr.
C) Werner Heisenberg.
D) Max Planck.
E) Paul Dirac.

Question 27

For an orbital angular momentum quantum number of 4, what is the magnitude of the orbital angular momentum?

A) 4ℏ
B) 3ℏ
C) 6^1/2ℏ
D) 12^1/2ℏ
E) 20^1/2ℏ

Question 28

If a string of length L, fixed at both ends, is made to resonate at its lowest possible frequency, what is the wavelength associated with that resonance?

A) L
B) 2L
C) L/2
D) 0.707 L
E) 1.414 L

Question 29

A particle in a box with ground-state energy E₁ = 4.0 eV undergoes a transition from the third excited state to the second excited state, emitting a photon in the process. What is the energy of the photon?

A) 4.0 eV
B) 16 eV
C) 20 eV
D) 28 eV
E) 26 eV

Question 30

Instead of the usual position-momentum formulation, an alternate version of the uncertainty principle relates what two quantities?

A) mass and angular momentum
B) charge and electric field
C) angle and position
D) energy and time
E) wavelength and frequency

Question 31

If light of wavelength 600 nm is used to locate an electron to within one wavelength of the light, what is the minimum uncertainty in the electron's momentum?

A) 1.1 × 10⁻²⁷ kg·m/s
B) 1.8 × 10⁻²⁸ kg·m/s
C) 8.8 × 10⁻²⁹ kg·m/s
D) 1.2 × 10⁻³² kg·m/s
E) 1.8 × 10⁻³² kg·m/s

Question 32

Which of these statements about electron energy levels in hydrogen atoms is true?

A) An electron with a positive total energy is a bound electron.
B) The orbital angular momentum of an electron in the ground state is zero.
C) An electron in the hydrogen atom is best represented as a traveling wave.
D) An electron in state n can make transitions only to the state n + 1 or n − 1.

Question 33

If a particle in a box has a ground-state energy of 10.0 eV, what is the energy of the fourth excited state?

A) 20.0 eV
B) 40.0 eV
C) 160 eV
D) 50.0 eV
E) 250 eV

Question 34

How many quantum numbers are required to specify the state of the electron in the hydrogen atom?

A) 1
B) 2
C) 3
D) 4
E) 5

Question 35

The statistical interpretation of the wave function originated with

A) Max Born.
B) Niels Bohr.
C) Albert Einstein.
D) Erwin Schrödinger.
E) Max Planck.

Question 36

In a 3d subshell, what are the possible values for the orbital magnetic quantum number?

A) 3
B) 3, −3
C) 3, 2, 1, 0
D) 2, 1, 0, −1, −2
E) 2, −2

Question 37

If the orbital angular momentum quantum number is 3, how many values are possible for the orbital magnetic quantum number?

A) 9
B) 7
C) 5
D) 4
E) 3

Question 38

For the principal quantum number n = 4, how many values can the orbital angular momentum quantum number have?

A) 9
B) 5
C) 4
D) 3
E) 32

Question 39

For a particle in a finite box, which of the following is false?

A) The energies are quantized for bound states.
B) The bound-state wave functions at the walls do not have to be zero.
C) The wave function can exist outside the walls.
D) There are the same number of bound states in a finite box as in a box with infinite walls.

Question 40

According to the uncertainty principle, if the uncertainty in position is reduced by a factor of two, the minimum uncertainty in momentum

A) halves.
B) quarters.
C) doubles.
D) quadruples.
E) doesn't change.

Question 41

Alkali metals have how many electrons past the noble gas configuration?

A) 1
B) 2
C) 3
D) 4
E) 5

Question 42

The Pauli exclusion principle

A) excludes electrons from atomic nuclei.
B) means that no two electrons in an atom can have the same orbit.
C) implies that no two electrons in an atom can have identical sets of quantum numbers.
D) excludes protons from electron orbits.

Question 43

The configuration 1s²2s²2p⁶3s²3p¹ is for what element?

A) B
B) F
C) Ne
D) Al
E) Cr

Question 44

A carbon dioxide laser emits photons of 10.6 μm wavelength. How many photons per second are emitted by a 10.0 kW CO₂ laser?

A) 4.27 × 10²¹
B) 5.39 × 10³⁰
C) 3.17 × 10¹⁸
D) 5.34 × 10²³
E) 6.20 × 10²³

Question 45

If the ground-state configuration of an atom is 1s²2s²2p⁴, what is the atomic number of the atom?

A) 14
B) 10
C) 8
D) 4
E) 3

Question 46

The de Broglie wavelength for a particle is related to its

A) position.
B) momentum.
C) mass.
D) charge.

Question 47

In the He-Ne laser, the lasing transition goes from the metastable 20.66 eV state in Ne to a lower-energy state. The wavelength of the laser photons is 633.0 nm. What is the energy of the lower state of the lasing transition?

A) 0
B) 4.660 eV
C) 13.61 eV
D) 18.70 eV
E) 20.61 eV

Question 48

Excited atomic states that last for a relatively long time are called

A) laser states.
B) metastable states.
C) amplification states.
D) radiation states.
E) cascading states.

Question 49

Except for helium, the outer subshell of a noble gas has what electronic configuration?

A) s²
B) p⁶
C) d¹⁰
D) p²
E) s¹p⁴

Question 50

What is the approximate average thermal energy of an electron in a solid at room temperature?

A) 0.00
B) 0.0010 eV
C) 0.025 eV
D) 27 eV
E) 1.0 keV

Question 51

Optical pumping of a ruby laser is achieved using photons of energy 2.25 eV. The laser light consists of photons of energy 1.79 eV, emitted in a transition that goes to ground. What is the energy of the transition from the pumped stated to the metastable state?

A) 2.25 eV
B) 1.79 eV
C) 4.04 eV
D) 0.46 eV
E) 1.30 eV

Question 52

What letter stands for a subshell with orbital angular momentum quantum number 5?

A) h
B) g
C) f
D) d
E) p

Question 53

A situation known as "population inversion" is needed for lasing action. What does "population inversion" mean?

A) Electrons in the ms = 1/2 state switch to −1/2 and vice versa.
B) Excited atoms must be at the top of the laser tube.
C) Excited atoms must be at the bottom of the laser tube.
D) More atoms are in the higher-energy state than the lower-energy state.
E) More atoms are in the lower-energy state than the higher-energy state.

Question 54

An atom has the configuration 1s²2s²2p⁶3s²3p⁶4s²3d¹⁰ in the ground state. What is its atomic number?

A) 10
B) 18
C) 20
D) 30
E) More information is needed.

Question 55

How many states are in the n = 4 shell?

A) 4
B) 9
C) 16
D) 18
E) 32

Question 56

If an element has a band gap of 1 eV between a filled valence band and an empty conduction band, it would be classified (at room temperature) as a(n)

A) insulator.
B) conductor.
C) resistor.
D) semiconductor.
E) reactor.

Question 57

If a solid has a half-filled valence band, which of the following would it be?

A) a conductor
B) an insulator
C) a semiconductor
D) a p-type semiconductor
E) an n-type semiconductor

Question 58

For the principal quantum number n = 5, what is the greatest number of values the spin magnetic quantum number can have?

A) 5
B) 25
C) 11
D) 2
E) 4

Question 59

What is the orbital angular momentum quantum number for a d subshell?

A) 10
B) 7
C) 4
D) 3
E) 2

Question 60

The word laser is an acronym for

A) light amplification by stimulated emission of radiation.
B) lighting by advanced showers of energetic rays.
C) local atomic spectroscopy for emission and ranging.
D) loop axial staged emergence radiometer.
E) large area scanning electron repeater.

Question 61

As the principal quantum number for a particle in the infinite square well increases, what happens to the spacing between adjacent energy levels?

A) It decreases.
B) It stays the same.
C) It increases.

Question 62

A baseball has a mass of 0.15 kg. If pitched at 40.0 m/s with a relative uncertainty of 1%, how uncertain is its position?

A) 8.8 × 10⁻³⁴ m
B) 1.1 × 10⁻³⁴ m
C) 1.8 × 10⁻³³m
D) 1.1 × 10⁻³²m

Question 63

A beam of neutrons (m = 939.6 MeV/c²) of momentum 12 keV/c is passed through a single slit of width 0.1 nm. As a result of this, the neutron beam acquires an uncertainty in the component of the momentum that is transverse to the beam direction. The distance between the slit and a screen onto which the neutrons are projected is 1.5 m. Using the uncertainty principle, estimate the expected width of the neutron distribution on the screen.

A) 0.1 mm
B) 1 cm
C) 50 cm
D) 5 m

Question 64

What is the full multiplicity (number of states) of the n = 3 level of the H atom?

A) 18
B) 30
C) 16
D) 32
E) 9

Question 65

How many different spin orientations can an electron have in a given orbital?

A) 2
B) 1
C) any number
D) 4

Question 66

The uncertainty in the position of a proton is 250 pm. Estimate the kinetic energy of the proton.

A) 1.3 × 10⁻²³ eV
B) 8.3 × 10⁻⁵ eV
C) 0.013 eV
D) 0.24 eV
E) 100 MeV

Question 67

As the principal quantum number of the hydrogen atom increases, what happens to the spacing between adjacent energy levels?

A) It decreases.
B) It increases.
C) It stays the same.

Question 68

You would like to use an electron microscope to study features of a virus that are about 0.25 nm in size. What accelerating voltage is needed for the electrons in this microscope?

A) 96 V
B) 48 V
C) 24 V
D) 5 V

Question 69

For the first excited state (n = 2) of the particle in a box of width L, what is the approximate uncertainty in momentum?

A) 3h/L
B) 2h/L
C) h/L
D) h/2L

Question 70

Each element in a column of the periodic table

A) has a similar size.
B) has similar nuclear properties.
C) has a similar electronic configuration.
D) has a similar nuclear charge.

Question 71

The energy of an electron in an atom depends primarily on

A) the spin magnetic quantum number m_s.
B) the principal quantum number n.
C) the orbital angular momentum quantum number l.
D) the orbital magnetic quantum number ml.

Question 72

The uncertainty in the position of a proton is 250 pm. Estimate the velocity of the proton.

A) 0.01 m/s
B) 1.6 m/s
C) 130 m/s
D) 1.6 × 10³ m/s
E) 1.3 × 10⁵ m/s

Question 73

The more precisely the position of a particle is known,

A) the more precisely its momentum can be known.
B) the more precisely its energy can be known.
C) the less precisely its momentum can be known.
D) the shorter its de Broglie wavelength is.