Deck 42: Atomic Physics

Question 1

In the subshell of the Li²⁺ ion with orbital quantum number , the allowed values of the magnetic quantum number are

A) − to
B) −( + 1)to( + l)
C) − ( + 2) to ( + 2)
D) −( + 3) to ( + 3)
E) 0 to n − 1

Answer 1

− to

Question 2

Suppose Bohr had chosen the potential energy of the electron in the hydrogen atom to be V = 0 when the electron is in the orbit with n = 1. He could do this by

A) choosing n = 1 for the orbit where the kinetic energy of the electron is zero.
B) adding a constant 13.6 eV to the potential energy for all values of n.
C) adding a constant 27.2 eV to the potential energy for all values of n.
D) subtracting a constant 13.6 eV from the potential energy for all values of n.
E) subtracting a constant 27.2 eV from the potential energy for all values of n.

Answer 2

adding a constant 27.2 eV to the potential energy for all values of n.

Question 3

The energy needed to remove an electron from the first excited state of a Li²⁺ ion is

A) 53 eV
B) 31 eV
C) 92 eV
D) 122 eV
E) 61 eV

Answer 3

31 eV

Question 4

In a shell of the hydrogen atom with n = 3, the permitted values of the orbital magnetic quantum number are

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

Question 5

Of the following states, 5s, 3p, 4f, 5p, 4g, 3d, and 2p, the one which is NOT allowed is

A) 3p
B) 4f
C) 3d
D) 4g
E) 2p

Question 6

The allowed values of for the n = 3 shell in a Li²⁺ ion are

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

Question 7

The K, L, M symbols represent values of the quantum number

A) n
B)
C)
D) m_s
E) m_j

Question 8

What wavelength (in μm) is associated with the Paschen series for n = 4?
(R_H = 1.097 × 10⁷ m−¹)

A) 320
B) 530
C) 2.7
D) 1.9
E) 0.5

Question 9

The allowed values of n for the Li²⁺ ion are

A) 1 to ∞
B) 2 to ∞
C) 3 to ∞
D) any real number
E) 1 to 10

Question 10

An electron is moving at a speed of 2.1 × 10⁶ m/s in the first Bohr orbit. Determine its de Broglie wavelength.

A) 0.30 × 10−¹⁰ m
B) 1.7 × 10−¹⁰ m
C) 0.50 × 10−¹⁰ m
D) 3.5 × 10−¹⁰ m
E) 1.5 × 10−¹⁰ m

Question 11

How fast is the electron moving in the first Bohr orbit?

A) 3.3 × 10⁶ m/s
B) 2.2 × 10⁶ m/s
C) 4.4 × 10⁶ m/s
D) 5.5 × 10⁶ m/s
E) 5.5 × 10¹⁵ m/s

Question 12

An energy of 13.6 eV is needed to ionize an electron from the ground state of a hydrogen atom. Selecting the longest wavelength that will work from the those given below, what wavelength is needed if a photon accomplishes this task?

A) 60 nm
B) 80 nm
C) 70 nm
D) 90 nm
E) 40 nm

Question 13

What value of wavelength is associated with the Lyman series for n = 2?
(R_H = 1.097 × 10⁷ m−¹)

A) 8.2 × 10⁶ m
B) 1.2 × 10−⁷ m
C) 2.7 × 10⁶ m
D) 3.6 × 10−⁷ m
E) 8.8 × 10−⁷ m

Question 14

An electron in a hydrogen atom makes a transition from the n = 4 to the n = 3 energy state. Determine the energy (in eV) of the emitted photon.

A) 0.54
B) 0.66
C) 0.85
D) 1.51
E) 10.2

Question 15

An electron in a hydrogen atom makes a transition from the n = 3 to the n = 1 energy state. Determine the wavelength of the emitted photon (in nm).

A) 1006
B) 209
C) 306
D) 103
E) 821

Question 16

One of the main problems with the Bohr model of the hydrogen atom when compared with the results of the methods of quantum mechanics used to describe atoms, was that the Bohr model predicted

A) the ground state angular momentum was L = 1
.
B) the frequency of the radiation emitted when an electron "jumps" from one allowed orbit to another was hf = E_i − E_f.
C) the potential energy function for the hydrogen atom was given by V(r) = −ke²/r.
D) the energy of the ground state of the hydrogen atom was E_n = −13.6 eV.

Question 17

The s, p, d, f, symbols represent values of the quantum number

A) m_s
B) n
C)

D)

E) m_j

Question 18

A hydrogen atom is in its first excited state (n = 2). The linear momentum of the electron is (in kg ⋅ m/s)

A) 3 × 10−²⁴
B) 2 × 10−²⁴
C) 1 × 10−²⁴
D) 4 × 10−²⁴
E) 3 × 10−¹⁵

Question 19

The number of states in the He⁺ ion corresponding to the principle quantum number n = 5 are

A) 18
B) 25
C) 50
D) 9
E) 11

Question 20

Light is emitted by hydrogen atoms in the visible range for a hydrogen atom. Its wavelength is 656 nm. What value of n is associated with the light? (R_H = 1.097 × 10⁷ m−¹)

A) 5
B) 2
C) 4
D) 3
E) 6

Question 21

Characteristic x-rays can be produced by bombarding targets with electrons. These x-rays occur when

A) electrons from higher shells fill the vacant lower shell
B) electrons fill the vacant valence shell
C) photons are emitted with energies on the order of 10³ eV
D) photons are emitted with wavelengths on the order of 10³ nm

Question 22

The energy needed to change a He⁺ ion in the ground state into a He²⁺ ion is

A) 13.6 eV
B) 54.4 eV
C) 112.4 eV
D) 92.9 eV
E) 27.2 eV

Question 23

A hydrogen atom in the 4f state has a total angular momentum (in terms of ) of magnitude

A)
B) 3
C) 6
D) 12

Question 24

In 1921, Stern and Gerlach performed an experiment that first demonstrated

A) orbital angular momentum quantization
B) energy quantization
C) space quantization
D) magnetic orbital quantization
E) that particles behave like waves

Question 25

Which of the following statements is true?

A)
can never be perpendicular to
.
B)
can be aligned parallel to
.
C)
must be perpendicular to
.
D)
can never be aligned parallel to
.

Question 26

When using the Pauli Exclusion Principle, we assume the particle's spin angular momentum is of magnitude

A)

B)

C)

D) ±

E)

Question 27

The radial portion of the de Broglie wavefunction for an electron in the ground state of the hydrogen atom is Ψ_1s(r) = 1/( )^1/2 exp(−r/a₀) where a₀ is the Bohr radius. The probability of finding the electron is

A)

B)

C)

D)

E)

Question 28

A Li²⁺ ion undergoes a transition from the n = 4 to the n = 3 state. The energy of the emitted photon is

A) 4.5 eV
B) 10.2 eV
C) 5.95 eV
D) 2.6 eV
E) 0.66 eV

Question 29

The probability density for the 1s state is given by |Ψ_1s|². The probability of finding the particle somewhere in space is

A)

B)

C)

D)

E)

Question 30

Rubidium (Z = 37) and potassium (Z = 19) are similar to sodium in that they have ____ electron(s) in the outermost shell.

A) five p
B) three p
C) two s
D) one d
E) one s

Question 31

If P(r) is the radial probability density function for an electron in the ground state of a hydrogen atom, the most probable value for r can be found from

A) dP/dt
B) dP/dr
C)

D)

E) d²P/dr²

Question 32

The probability density of a particle at a distance r from the nucleus is essentially the

A) probability of finding the particle within a small volume about r.
B) probability per unit area of finding the particle within a unit area centered on r.
C) probability per unit length of finding the particle within a unit length of r.
D) probability per unit volume of finding the particle within a small volume about r.
E)

Question 33

The magnitude of the spin angular momentum for an electron is equal to

A)

B)

C)
/2
D) ±
/2
E)

Question 34

Forbidden transitions and selection rules suggest that

A) a photon has linear momentum.
B) a photon has energy.
C) a photon has angular momentum.
D) a photon has parity.
E) a photon has mass.

Question 35

When electrons fill a subshell in which the orbitals have equal energy, the order in which the orbitals are filled is such that

A) a minimum number of electrons has unpaired spins.
B) a minimum number of electrons has intrinsic angular momentum.
C) a maximum number of electrons has unpaired spins.
D) a maximum number of electrons first fills the next energy level.
E) the maximum number of electrons has the same set of quantum numbers.

Question 36

For the following allowed transitions, which photon would have the largest wavelength when an electron "jumps" from one energy level, characterized by the quantum number n, to another?

A) n = 2 to n = 1
B) n = 3 to n = 2
C) n = 3 to n = 1
D) n = 1 to n = 3
E) n = 4 to n = 1

Question 37

What angle does the orbital angular momentum make with the z axis of a hydrogen atom in the state n = 3, = 2, = −1?

A) −66°
B) 66°
C) 24°
D) 114°
E) 73°

Question 38

The ground state configuration of chlorine (Z = 17) is

A) 1s² 2s² 2p⁵ 3s² 3p⁶
B) 1s² 2s² 2p⁶ 3s² 3p⁵
C) 1s² 2s² 2p⁶ 3s² 3p⁴ 3d¹
D) 1s² 2s² 2p⁶ 3s² 3p⁵ 4s¹
E) 1s² 2s² 2p⁶ 3s¹ 3p⁷

Question 39

In a completely filled atomic shell,

A) the intrinsic spin of the electrons does not produce a resultant magnetic moment.
B) the orbital motion of the electrons does not produce a resultant magnetic moment.
C) the atom will be an alkali metal.
D) only (a) and (b) are correct.
E) none of the above are correct.

Question 40

The Pauli Exclusion Principle states

A) no two electrons in the same atom can have the same set of quantum numbers.
B) there is an inherent uncertainty in the position and momentum of a particle.
C) when an atom has orbitals of equal energy, the maximum number of electrons will have unpaired spins.
D) when an atom has orbitals of equal energy, the maximum number of electrons will be paired spins.
E) no two atoms can have the same set of quantum numbers.

Question 41

Which of the following, in which n and m have integer values, is a correct formula for a wavelength emitted by a hydrogen atom?

A)

B)

C)

D)

E)

Question 42

What is the difference in frequency for spectral lines emitted by hydrogen for transitions from the n = 16 level to the n = 2 level and transitions from the n = 15 level to the n = 2 level? (R_H = 1.097 × 10⁷ m−¹.)

A) 5.65 × 10−¹³ Hz
B) 31 Hz
C) 1.77 × 10¹² Hz
D) 2.55 × 10¹⁶ Hz
E) 1.02 × 10¹⁷ Hz

Question 43

A hydrogen atom emits a photon of wavelength 657.7 nm. From what energy state to what lower energy state did the electron jump?

Question 44

A headwaiter at a restaurant decides to apply the exclusion principle to the seating of patrons. He will treat tables as sub-shells, and will only seat patrons if the number of the people to be seated adds up to a complete sub-shell. Of the numbers below, the number he would not be willing to seat at one table is

A) 2.
B) 4.
C) 6.
D) 10.
E) 14.

Question 45

Quantum physics agrees with the classical physics limit when

A) the total angular momentum is a small multiple of
.
B) the total energy is a small multiple of the energy in the lowest quantized state.
C) the difference in energy between adjacent quantized levels becomes vanishingly small.
D) all electron spins are paired so that L = 0.
E) there is a vacancy in an inner level in the atom.

Question 46

Adam and Eve are contemplating the beauty of the hydrogen atom. Adam claims that the quantum states with a given value of the principal quantum number n can have any value of the orbital quantum number . Eve says that the Snake told her that a state with a given value of could have any value of n. Which one, if either, is correct, and why?

A) Adam, because the man is always right.
B) Adam because n ≤
− 1.
C) Eve, because n ≤
− 1.
D) Eve, because
≤ n − 1.
E) Neither, because Adam is wrong and the Snake told a subtle lie.

Question 47

The energy difference between the upper and lower levels in a certain laser is 1.9593 eV. What is the wavelength of the light emitted by the laser?

Question 48

What is the difference in wavelength for spectral lines emitted by hydrogen for transitions from the n = 16 level to the n = 2 level and transitions from the n = 15 level to the n = 2 level? (R_H = 1.097 × 10⁷ m−¹.)

A) 1.0 × 10−¹⁰ m
B) 2.0 × 10−¹⁰ m
C) 4.1 × 10−¹⁰ m
D) 8.1 × 10−¹⁰ m
E) 1.6 × 10−⁹ m

Question 49

Aline says that the magnetic moment of an atom originates in the orbital angular momentum of the electron. Bevis says that it comes from the electron spin. Which one, if either, is correct, and why?

A) Aline, because only atoms, not electrons, can have angular momentum.
B) Bevis, because only atoms, not electrons, can have angular momentum.
C) Neither, because electron spin and orbital angular momentum always cancel exactly.
D) Neither, because the magnetic moment of an atom comes only from the spin of the nucleus.
E) Both, because both the orbital angular momentum and the spins of the electrons contribute to the magnetic moment of an atom.

Question 50

The number of electrons in the n = 4, = 2 subshell in strontium (Z = 38) is ____ the number of electrons in the n =4, =2 subshell in barium (Z = 56).

A)
times
B)
times
C) equal to
D)
times
E)
times

Question 51

In the Bohr model of the hydrogen atom, the total energy of the electron-proton system is

A)
.
B)
.
C) 0.
D)
.
E)
.

Question 52

Suppose a beam of electrons is incident on a collection of hydrogen atoms, all of which are in the lowest energy state (n = 1). What is the minimum energy the electrons can have if they are to excite the hydrogen atoms into the n = 2 state?

Question 53

In an atom that has an electron in a sub-shell for which = 4, with respect to the magnetic field vector the magnetic moment vector of the electron is allowed to be oriented in

A) any direction.
B)
discrete directions
C)
− 1 discrete directions.
D)
+ 1 discrete directions.
E) 2
+ 1 discrete directions.

Question 54

In an allowed electron transition in a hydrogen atom,

A) Δ
= 0;
= 0, ±1.
B) Δ
= 0, ±1;
= ±1.
C) Δ
= 0, ±1;
= 0, ±1.
D) Δ
= ±1;
= 0, ±1.
E) Δ
= ±1;
= ±1.

Question 55

In the operation of a laser

A) stimulated emission occurs.
B) there is a population inversion.
C) the excited state will tend to be metastable.
D) the photons emitted will have transitioned to the ground state.
E) For the answers (a), (b), (c), and (d), three are correct and one is incorrect.

Question 56

All quantum states forming a shell have the same

A) principal quantum number n.
B) orbital quantum number
.
C) orbital magnetic quantum number
.
D) n,
and

E) n and
only.

Question 57

In terms of a₀, where a₀ = 0.0529 nm, the radii of the allowed orbits in the Bohr model of the hydrogen atom are given by r_n =

A)
.
B)
.
C)
.
D) na₀.
E) n²a₀.

Question 58

Zeke says that the magnitude of the orbital angular momentum in the hydrogen atom has the value L = . Ruth says that the maximum magnitude of the projection of the angular momentum along the direction of a constant magnetic field vector is . Which one, if either, is correct, and why?

A) Ruth, because the maximum value of L is
.
B) Ruth, because the orbital angular momentum always lines up with a magnetic field so that
has its maximum value along the field.
C) Zeke, because the maximum magnitude of
is L =
.
D) Zeke, because the orbital angular momentum always lines up with a magnetic field so that
has its maximum value along the field.
E) Neither, because they have interchanged the maximum magnitude of
,
, and
, its maximum projection along a magnetic field direction.

Question 59

All quantum states forming a sub-shell have the same

A) principal quantum number n.
B) orbital quantum number
.
C) orbital magnetic quantum number
.
D) n,
and

E) n and
only.