Deck 40: All About Atoms

Question 1

The Einstein-de Haas experiment showed that:

A) atoms emit and absorb light, but only of certain wavelengths.
B) atoms have momentum, and momentum is conserved.
C) atoms have electric fields, and electric fields can cause their energy levels to split.
D) atoms have magnetic dipole moments that are coupled to their angular momentum.
E) a gradient in a magnetic field will cause a beam of atoms to split.

Answer 1

atoms have magnetic dipole moments that are coupled to their angular momentum.

Question 2

The magnitude of the orbital magnetic dipole moment of an atom is ( $\mu$ _B is the Bohr magneton, and ℓ is a positive integer):

A) $\mu$ _B
B) $\mu$ _B ℓ
C)
D) $\mu$ _B (2ℓ+1)
E) $\mu$ _B ℓ²

Answer 2

Question 3

The magnetic quantum number m_ℓ is most closely associated with what property of the electron in an atom?

A) Magnitude of the orbital angular momentum
B) Energy
C) z component of the spin angular momentum
D) z component of the orbital angular momentum
E) Radius of the orbit

Answer 3

z component of the orbital angular momentum

Question 4

The number of states in a subshell with orbital quantum number ℓ=3 is:

A) 2
B) 3
C) 7
D) 9
E) 14

Question 5

The quantity L_z is related to the quantum number m_ℓ by:

A)
B)
C)
D)
E)

Question 6

The number of values of the orbital quantum number ℓ associated with the principal quantum number n = 3 is:

A) 1
B) 2
C) 3
D) 4
E) 7

Question 7

The electron states in an atom which constitute a single shell all have:

A) the same value of n
B) the same value of ℓ
C) the same value of n and the same value of ℓ
D) the same value of ℓ and the same value of m_ℓ
E) the same set of all four quantum numbers

Question 8

Possible values of the principal quantum number n for an electron in an atom are:

A) only 0 and 1
B) only 0,1,2,..., $\infty$
C) only 0,1,..., ℓ−1
D) only 1/2 and -1/2
E) only 1,2,3,..., $\infty$

Question 9

The quantum number m_s is most closely associated with what property of the electron in an atom?

A) Magnitude of the orbital angular momentum
B) Energy
C) z component of the spin angular momentum
D) z component of the orbital angular momentum
E) Radius of the orbit

Question 10

An atom is in a state with orbital quantum number ℓ=2. Possible values of the magnetic quantum number m_ℓ are:

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

Question 11

The number of states in a shell with principal quantum number n = 3 is:

A) 3
B) 8
C) 9
D) 18
E) 32

Question 12

The number of possible values of the magnetic quantum number m_ℓ associated with a given value of the orbital quantum number ℓ is:

A) 1
B) 2
C) ℓ
D) 2 ℓ
E) 2 ℓ +1

Question 13

The electron states in an atom which constitute a single subshell all have:

A) only the same value of n
B) only the same value of ℓ
C) only the same value of n and the same value of ℓ
D) only the same value of ℓ and the same value of m_ℓ
E) the same set of all four quantum numbers

Question 14

An electron in an atom is in a state with principal quantum number n = 4. The possible values of the orbital quantum number ℓ are:

A) 1, 2, 3
B) 1, 2, 3, 4
C) -3, -2, -1, 0, 1, 2, 3
D) 0, 1, 2, 3
E) 0, 1, 2

Question 15

The magnitude of the orbital angular momentum of an electron is what multiple of ? (ℓ is a positive integer.)

A) 1
B) 1/2
C)
D) 2ℓ+1
E) ℓ²

Question 16

The possible values for the magnetic quantum number m_s of an electron in an atom:

A) depend on n
B) depend on ℓ
C) depend on both n and ℓ
D) depend on whether or not there is an external magnetic field present
E) are $\pm$ 1/2

Question 17

An electron is in a quantum state for which there are seven allowed values of the z component of the angular momentum. The magnitude of the angular momentum is:

A)
B)
C)
D)
E)

Question 18

An electron is in a quantum state for which the magnitude of the orbital angular momentum is . How many allowed values of the z component of the angular momentum are there?

A) 7
B) 8
C) 16
D) 17
E) 20

Question 19

The total number of electron states with n = 2 and ℓ=1 for an atom is:

A) 2
B) 4
C) 6
D) 8
E) 10

Question 20

Space quantization means that:

A) space is quantized
B) L_z can have only certain discrete values
C) and are in the same direction
D) and are in opposite directions
E) an electron has a magnetic dipole moment

Question 21

The magnetic field is along the z axis in a Stern-Gerlach experiment. The force it exerts on a magnetic dipole with dipole moment is proportional to:

A)
B) B²
C) dB/dz
D) d²B/dz²
E) $\int$ B dz

Question 22

Electrons are in a two-dimensional square potential energy well with sides of length L. The potential energy is infinite at the sides and zero inside. The single-particle energies are given by where n_x and n_y are integers. The number of single-particle states with energy 5(h²/8mL²) is:

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

Question 23

The Pauli exclusion principle is obeyed by:

A) all particles
B) all charged particles
C) all particles with spin quantum numbers of 1/2
D) all particles with spin quantum numbers of 1
E) all particles with mass

Question 24

Five electrons are in a two-dimensional square potential energy well with sides of length L. The potential energy is infinite at the sides and zero inside. The single-particle energies are given by where n_x and n_y are integers. The energy of the ground state of the system is

A) 0
B) 10 (h²/8mL²)
C) 19 (h²/8mL²)
D) 24 (h²/8mL²)
E) 48 (h²/8mL²)

Question 25

When a lithium atom is made from a helium atom by adding a proton (and neutron) to the nucleus and an electron outside, the electron goes into an n = 2, ℓ=0 state rather than an n = 1, ℓ=0 state. This is an indication that electrons:

A) obey the Pauli exclusion principle
B) obey the minimum energy principle
C) undergo the Zeeman effect
D) are diffracted
E) and protons are interchangeable

Question 26

The figure shows two different orientations of a proton in a magnetic field. Which orientation is at higher energy?

A) a
B) b
C) Both are at the same energy, and there is no other orientation at higher energy.
D) Both are at the same energy, but if the spin vector were perpendicular to the magnetic field the energy would be higher.
E) Both are at the same energy, but if the spin vector were perpendicular to the magnetic field the energy would be lower.

Question 27

A magnetic dipole is placed in a strong uniform magnetic field The associated force e exerted on the dipole is:

A)
B)
C) along
D) along
E) zero

Question 28

An electron in an atom is in a state with ℓ=3 and m_ℓ =2. The angle between and the z axis is:

A) 30 $\degree$
B) 35.3 $\degree$
C) 48.2 $\degree$
D) 54.7 $\degree$
E) 60 $\degree$

Question 29

The magnitude of the spin magnetic dipole moment of an atom is ( $\degree$ _B is the Bohr magneton, and s is a positive number):

A) $\degree$ _B
B) $\degree$ _B s
C)
D)
E) 2 $\degree$ _B s

Question 30

No state in an atom can be occupied by more than one electron. This is most closely related to the:

A) wave nature of matter
B) finite value for the speed of light
C) Bohr magneton
D) Pauli exclusion principle
E) the Einstein-de Haas effect

Question 31

A magnetic dipole is placed between the poles of a magnet as shown. The direction of the associated force exerted on the dipole is:

A) positive x
B) positive y
C) negative x
D) negative y
E) into or out of the page

Question 32

Hydrogen atoms are in a magnetic field of 2.0 T. What is their magnetic resonance frequency?

A) 2.8 x 10¹⁰ Hz
B) 5.6 x 10¹⁰ Hz
C) 1.1 x 10¹¹ Hz
D) 1.8 x 10¹¹ Hz
E) 3.5 x 10¹¹ Hz

Question 33

Six electrons are in a two-dimensional square potential energy well with sides of length L. The potential energy is infinite at the sides and zero inside. The single-particle energies are given by where n_x and n_y are integers. If a seventh electron is added to the system when it is in its ground state the least energy the additional electron can have is:

A) 2 (h²/8mL²)
B) 5 (h²/8mL²)
C) 8 (h²/8mL²)
D) 10 (h²/8mL²)
E) 13 (h²/8mL²)

Question 34

The quantity s_z is related to the quantum number m_s by:

A)
B)
C)
D)
E)

Question 35

In the relation µ_z=−m_ℓµ_B, the quantity $\mu$ 0_B is:

A) the Bohr magneton
B) the component of the dipole moment along the magnetic field
C) the permeability of the material
D) a friction coefficient
E) none of the above

Question 36

The force exerted on a magnetic dipole as it moves with velocity through a Stern-Gerlach apparatus is:

A) proportional to v
B) proportional to 1/v
C) zero
D) proportional to v²
E) independent of v

Question 37

Five electrons are in a two-dimensional square potential energy well with sides of length L. The potential energy is infinite at the sides and zero inside. The single-particle energies are given by where n_x and n_y are integers. The energy of the first excited state of the system is:

A) 13 (h²/8mL²)
B) 22 (h²/8mL²)
C) 24 (h²/8mL²)
D) 25 (h²/8mL²)
E) 27 (h²/8mL²)

Question 38

The Stern-Gerlach experiment makes use of:

A) a strong uniform magnetic field
B) a strong non-uniform magnetic field
C) a strong uniform electric field
D) a strong non-uniform electric field
E) strong perpendicular electric and magnetic fields

Question 39

An electron in an atom is in a state with ℓ=5. The minimum angle between and the z axis is:

A) 0 $\degree$
B) 18.0 $\degree$
C) 24.1 $\degree$
D) 33.6 $\degree$
E) 36.7 $\degree$

Question 40

Electrons are in a two-dimensional square potential energy well with sides of length L. The potential energy is infinite at the sides and zero inside. The single-particle energies are given by , , where n_x and n_y are integers. At most the number of electrons that can have energy 8(h²/8mL²) is:

A) 1
B) 2
C) 3
D) 4
E) any number

Question 41

A photon with the smallest wavelength in the continuous z-ray spectrum is emitted when:

A) an electron is knocked from a K shell
B) a valence electron is knocked from the atom
C) the incident electron becomes bound to the atom
D) the atom has the greatest recoil energy
E) the incident electron loses all its energy in a single decelerating event

Question 42

The transition shown gives rise to an x-ray. The correct label for this is:

A) K _$\alpha$
B) K _$\beta$
C) L _$\alpha$
D) L _$\beta$
E) KL

Question 43

Which of the following subshells cannot exist?

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

Question 44

The states being filled from the beginning to end of the lanthanide series of atoms are:

A) n = 3, ℓ=2 states
B) n = 4, ℓ=1 states
C) n = 4, ℓ=2 states
D) n = 4, ℓ=3 states
E) n = 5, ℓ=2 states

Question 45

Radiation with the minimum wavelength as well as the K x-ray lines are detected for a certain target. The energy of the incident electrons is then doubled, with the result that:

A) the minimum wavelength increases and the wavelengths of the K lines remain the same
B) the minimum wavelength decreases and the wavelengths of the K lines remain the same
C) the minimum wavelength and the wavelengths of the K lines all increase
D) the minimum wavelength and the wavelengths of the K lines all decrease
E) the minimum wavelength increases and the wavelengths of the K lines all decrease

Question 46

If electrons did not have intrinsic angular momentum (spin) but still obeyed the Pauli exclusion principle the states occupied by electrons in the ground state of helium would be:

A) (n = 1, ℓ=0); (n = 1, ℓ=0)
B) (n = 1, ℓ=0); (n = 1, ℓ=1)
C) (n = 1, ℓ=0); (n = 2, ℓ=0)
D) (n = 2, ℓ=0); (n = 2, ℓ=1)
E) (n = 2, ℓ=1); (n = 2, ℓ=1)

Question 47

The most energetic electron in any atom at the end of a period of the periodic table is in:

A) an ℓ=0 state
B) an ℓ=1 state
C) an ℓ=2 state
D) an n = 0 state with unspecified angular momentum
E) an n = 1 state with unspecified angular momentum

Question 48

The most energetic photon in a continuous x-ray spectrum has an energy approximately equal to:

A) the energy of all the electrons in a target atom
B) the kinetic energy of an incident-beam electron
C) the rest energy, mc², of an electron
D) the total energy of a K-electron in the target atom
E) the kinetic energy of a K-electron in the target atom

Question 49

The ionization energy of an atom in its ground state is:

A) the energy required to remove the least energetic electron
B) the energy required to remove the most energetic electron
C) the energy difference between the most energetic electron and the least energetic electron
D) the same as the energy of a K _$\alpha$ photon
E) the same as the excitation energy of the most energetic electron

Question 50

An electron in an L shell of an atom has the principal quantum number:

A) n = 0
B) n = 1
C) n = 2
D) n = 3
E) n = $\infty$

Question 51

In connection with x-ray emission the symbol K _$\alpha$ refers to:

A) an alpha particle radiation
B) an effect of the dielectric constant on energy levels
C) x-ray radiation from potassium
D) x-ray radiation associated with an electron going from n = $\infty$ to n = 1
E) x-ray radiation associated with an electron going from n = 2 to n = 1

Question 52

The group of atoms at the beginning of periods of the periodic table is called:

A) alkali metal atoms
B) rare earth atoms
C) transition metal atoms
D) alkaline atoms
E) noble gas atoms

Question 53

An electron in a K shell of an atom has the principal quantum number:

A) n = 0
B) n = 1
C) n = 2
D) n = 3
E) n = $\infty$

Question 54

Which of the following (n, ?, m_l , m_s) combinations is impossible for an electron in an atom?

A) 3, 1, 1, -1/2
B) 6, 2, 0, 1/2
C) 3, 2, -2, -1/2
D) 3, 1, -2, 1/2
E) 1, 0, 0, -1/2

Question 55

The most energetic electron in any atom at the beginning of a period of the periodic table is in:

A) an ℓ=0 state
B) an ℓ=1 state
C) an ℓ=2 state
D) an n = 0 state with unspecified angular momentum
E) an n = 1 state with unspecified angular momentum

Question 56

Characteristic K x-radiation of an element is caused by:

A) stoppage of electrons by the nucleus
B) scattering of the incident radiation with a change of wavelength
C) ejection of an electron from an outer shell
D) transition of an electron to the innermost orbit
E) none of the above

Question 57

In connection with x-ray emission the symbol L _$\beta$ refers to:

A) a beta particle radiation
B) an atomic state of angular momentum h/2 $\pi$
C) the inductance associated with an orbiting electron
D) x-radiation associated with an electron going from n = 4 to n = 2
E) none of the above

Question 58

Two different electron beams are incident on two different targets and both produce x rays. The cutoff wavelength for target 1 is shorter than the cutoff wavelength for target 2. We can conclude that:

A) target 2 has a higher atomic number than target 1
B) target 2 has a lower atomic number than target 1
C) the electrons in beam 1 have greater kinetic energy than those in beam 2
D) the electrons in beam 1 have less kinetic energy than those in beam 2
E) target 1 is thicker than target 2

Question 59

The group of atoms at the ends of periods of the periodic table is called:

A) alkali metal atoms
B) rare earth atoms
C) transition metal atoms
D) alkaline atoms
E) noble gas atoms

Question 60

For any atom other that hydrogen and helium all electrons in the same shell have:

A) the same energy
B) the same magnitude of angular momentum
C) the same magnetic quantum number
D) the same spin quantum number
E) none of the above

Question 61

Which of the following is essential for the laser action to occur between two energy levels of an atom?

A) the lower level is metastable
B) there are more atoms in the upper level than in the lower level
C) there are more atoms in the lower level than in the upper level
D) the lower level is the ground state
E) the lasing material is a gas

Question 62

In a laser:

A) excited atoms are stimulated to emit photons by radiation external to the laser
B) the transitions for laser emission are directly to the ground state
C) the states which give rise to laser emission are usually very unstable states that decay rapidly
D) the state in which an atom is initially excited is never between two states that are involved in the stimulated emission
E) a minimum of two energy levels are required.

Question 63

A laser beam can be sharply focused because it is:

A) highly coherent
B) plane polarized
C) intense
D) circularly polarized
E) highly directional

Question 64

Suppose the energy required to ionize a neon atom is i, the energy to excite it is e, and its energy due to thermal agitation at room temperature is t. In increasing order, these three energies are:

A) i, e, t
B) t, i, e
C) e, t, i
D) i, t, e
E) t, e, i

Question 65

In calculating the x-ray energy levels the effective charge of the nucleus is taken to be Z - b, where Z is the atomic number. The parameter b enters because:

A) an electron is removed from the inner shell
B) a proton is removed from the nucleus
C) the quantum mechanical force between two charges is less than the classical force
D) the nucleus is screened by electrons
E) the Pauli exclusion principle must be obeyed

Question 66

Which of the following is essential for laser action to occur between two energy levels of an atom?

A) the lower level is metastable
B) the upper level is metastable
C) the lower level is the ground state
D) the are more atoms in the lower level than in the upper level
E) the lasing material is a gas

Question 67

A laser must be pumped to achieve:

A) a metastable state
B) fast response
C) stimulated emission
D) population inversion
E) the same wavelength for all photons

Question 68

In a helium-neon laser, the laser light arises from a transition from a _________ state to a _________ state:

A) He, He
B) Ne, Ne
C) He, Ne
D) Ne, He
E) N, He

Question 69

In a Moseley graph:

A) the x-ray frequency is plotted as a function of atomic number
B) the square of the x-ray frequency is plotted as a function of atomic number
C) the square root of the x-ray frequency is plotted as a function of atomic number
D) the x-ray frequency is plotted as a function of the square root of atomic number
E) the square root of the x-ray frequency is plotted as a function of atomic mass

Question 70

The purpose of the mirrors at the ends of a helium-neon laser is:

A) to assure that no laser light leaks out
B) to increase the number of stimulated emissions
C) to absorb some of the photons
D) to keep the light used for pumping inside the laser
E) to double the effective length of the laser

Question 71

The ratio of wavelength of K _$\infty$ x-ray line for Nb (Z = 41) to that of Ga (Z = 31) is:

A) 9/16
B) 16/9
C) 3/4
D) 4/3
E) 1.15

Question 72

Photons in a laser beam have the same energy, wavelength, polarization direction, and phase because:

A) each is produced in an emission that is stimulated by another
B) all come from the same atom
C) the lasing material has only two quantum states
D) all photons are alike, no matter what their source
E) none of the above

Question 73

A group of electromagnetic waves might Which of these describe the waves from a laser?

A) I only
B) II only
C) III only
D) I and II only
E) I, II, and III

Question 74

Population inversion is important for the generation of a laser beam because it assures that:

A) spontaneous emission does not occur more often than stimulated emission
B) photons do not split too rapidly
C) more photons are emitted than are absorbed
D) photons do not collide with each other
E) photons do not make upward transitions

Question 75

A metastable state is important for the generation of a laser beam because it assures that:

A) spontaneous emission does not occur more often than stimulated emission
B) photons do not split too rapidly
C) more photons are emitted than are absorbed
D) photons do not collide with each other
E) photons do not make upward transitions

Question 76

Electrons in a certain laser make transitions from a metastable state to the ground state. Initially there are 6 F*10²⁰ atoms in the metastable state and 2 * 10²⁰ atoms in the ground state. The number of photons that can be produced in a single burst is about:

A) 2 * 10²⁰
B) 3 *10²⁰
C) 4 * 10²⁰
D) 6 * 10²⁰
E) 8 * 10²⁰

Question 77

The "e" in laser stands for:

A) electric
B) emf
C) energy
D) emission
E) entropy

Question 78

Photons in a laser beam are produced by:

A) transitions from a metastable state
B) transitions from a state that decays rapidly
C) splitting of other photons
D) pumping
E) reflection from mirrors

Question 79

The K _$\infty$ x rays arising from a cobalt (Z = 27) target have a wavelength of about 179 pm. The atomic number of a target that gives rise to K _$\infty$ x rays with a wavelength one-third as great ( $\approx$ 60pm) is:

A) Z = 9
B) Z = 26
C) Z = 28
D) Z = 46
E) Z = 81