Deck 29: Atomic Physics

Question 1

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) $\int _ { 0 } ^ { 2 } \Psi ^ { 2 } 4 \pi r ^ { 2 } d r$

Answer 1

probability per unit volume of finding the particle within a small volume about r.

Question 2

All quantum states forming a sub-shell have the same

A)principal quantum number n.
B)orbital quantum number $\ell$
C)orbital magnetic quantum number $m _ { t }$ .
D)n, $\ell$ and $m _ { t }$
E)n and $\ell$ only.

Answer 2

n and $\ell$ only.

Question 3

The probability density for the 1s state is given by | $\Psi$ _1s|².The probability of finding the particle somewhere in space is

A) $\int \left| \Psi _ { 1 s } \right| ^ { 2 } 4 \pi r ^ { 2 } d r$
B) $\int \left| \Psi _ { 1 s } \right| ^ { 2 } d r$
C) $\int \left| \Psi _ { 1 s } \right| ^ { 2 } r d r$
D) $\int \left| \Psi _ { 1 s } \right| ^ { 2 } r ^ { 2 } d r$
E) $\int \left| \Psi _ { 1 s } \right| ^ { 2 } r ^ { 3 } d r$

Answer 3

$\int \left| \Psi _ { 1 s } \right| ^ { 2 } 4 \pi r ^ { 2 } d r$

Question 4

In the subshell of the Li²⁺ ion with orbital quantum number $\ell$ ,the allowed values of the magnetic quantum number $m _ { t }$ are

A) $\ell$ to $\ell$
B)-( $\ell$ + 1)to ( $\ell$ + l)
C)-( $\ell$ + 2)to ( $\ell$ + 2)
D)-( $\ell$ + 3)to ( $\vec { B }$ + 3)
E)0 to n- 1

Question 5

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) $\int r P ( r ) 4 \pi r ^ { 2 } d r$
D) $\int r P ( r ) d r$
E)d²P/dr²

Question 6

The radial portion of the de Broglie wavefunction for an electron in the ground state of the hydrogen atom is $\Psi$ _1s(r)= 1/( $\pi a _ { 0 } ^ { 3 }$ )^1/2 exp(-r/a₀)where a₀ is the Bohr radius.The probability of finding the electron is

A) $\left( \pi / a _ { 0 } ^ { 3 } \right) \int \exp \left( - 2 r / a _ { 0 } \right) 4 \pi r ^ { 2 } d r$ .
B) $\left( \pi / a _ { 0 } ^ { 3 } \right) ^ { 1 / 2 } \int \exp \left( - 2 r / a _ { 0 } \right) 4 \pi r ^ { 2 } d r$
C) $\left( \pi / a _ { 0 } ^ { 3 } \right) ^ { 1 / 2 } \int \exp \left( - 2 r / a _ { 0 } \right) d r$
D) $\left( \pi / a _ { 0 } ^ { 3 } \right) ^ { 1 / 2 } \int \exp \left( - 2 r / a _ { 0 } \right) d r$ .
E) $\frac { d } { d r } \left[ \frac { 2 } { \pi a _ { 0 } ^ { 3 } } \exp \left( - 2 r / a _ { 0 } \right) \right] \left[ \frac { 1 } { \pi a _ { 0 } ^ { 3 } } \right] ^ { 1 / 2 } e ^ { - r / a ^ { 0 } 1 / 2 }$

Question 7

Which of the following statements is true?

A) $\overrightarrow { \mathbf { L } }$ can never be perpendicular to $\vec { B }$ .
B) $\overrightarrow { \mathbf { L } }$ can be aligned parallel to $\vec { B }$ .
C) $\overrightarrow { \mathbf { L } }$ must be perpendicular to $\vec { B }$ .
D) $\overrightarrow { \mathbf { L } }$ can never be aligned parallel to $\vec { B }$ .

Question 8

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 9

Quantum physics agrees with the classical physics limit when

A)the total angular momentum is a small multiple of $\hbar$ .
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 10

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

A)m_s
B)n
C) $m _ { t }$
D) $\ell$
E)m_j

Question 11

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 $\hbar$ .
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 12

All quantum states forming a shell have the same

A)principal quantum number n.
B)orbital quantum number $\ell$
C)orbital magnetic quantum number $m _ { t }$ .
D)n, $\ell$ and $m _ { t }$
E)n and $\ell$ only.

Question 13

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 $\ell$ .Eve says that the Snake told her that a state with a given value of $\ell$ 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 $\le$$\ell$ - 1.
C)Eve,because n $\le$ $\ell$ - 1.
D)Eve,because $\ell$ $\le$ n -1.
E)Neither,because Adam is wrong and the Snake told a subtle lie.

Question 14

The allowed values of $\ell$ 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 15

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 16

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 17

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) $\frac { 1 } { n ^ { 2 } } a _ { 0 }$ .
B) $\frac { a _ { 0 } } { n }$ .
C) $\sqrt { n } a _ { 0 }$ .
D)na₀.
E)n²a₀.

Question 18

In a shell of the hydrogen atom with n = 3,the permitted values of the orbital magnetic quantum number $m _ { t }$ 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 19

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

A)n
B) $\ell$
C) $\vec { B }$
D)m_s
E)m_j

Question 20

The allowed values of n for the Li²⁺ ion are

A)1 to $\infty$
B)2 to $\infty$
C)3 to $\infty$
D)any real number
E)1 to 10

Question 21

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 22

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 23

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 24

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 25

Zeke says that the magnitude of the orbital angular momentum in the hydrogen atom has the value L = $\ell\hbar$ .Ruth says that the maximum magnitude of the projection of the angular momentum along the direction of a constant magnetic field vector $\vec { B }$ is $\sqrt { \ell ( \ell + 1 ) } \hbar$ .Which one,if either,is correct,and why?

A)Ruth,because the maximum value of L is $\sqrt { \ell ( \ell + 1 ) } \hbar$ .
B)Ruth,because the orbital angular momentum always lines up with a magnetic field so that $\overrightarrow { \mathbf { L } }$ has its maximum value along the field.
C)Zeke,because the maximum magnitude of $\overrightarrow { \mathbf { L } }$ is L = $\ell\hbar$ .
D)Zeke,because the orbital angular momentum always lines up with a magnetic field so that $\overrightarrow { \mathbf { L } }$ has its maximum value along the field.
E)Neither,because they have interchanged the maximum magnitude of $\overrightarrow { \mathbf { L } }$ , $\sqrt { \ell ( \ell + 1 ) } \hbar$ ,and $\ell\hbar$ ,its maximum projection along a magnetic field direction.

Question 26

What angle does the orbital angular momentum make with the z axis of a hydrogen atom in the state n = 3, $\ell$ = 2, $m _ { t }$ = -1?

A)-66 $\degree$
B)66 $\degree$
C)24 $\degree$
D)114 $\degree$
E)73 $\degree$

Question 27

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

A) $\sqrt { 3 } \hbar$
B) $\frac { \sqrt { 3 } } { 2 } \hbar$
C) $\hbar$ /2.
D) $\hbar$ /2
E) $\frac { 3 } { 4 } \hbar$

Question 28

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 29

In an allowed electron transition in a hydrogen atom,

A) $\Delta$ $\ell$ = 0; $m _ { t }$ = 0, $\pm$ 1.
B) $\Delta$ $\ell$ = 0, $\pm$ 1; $m _ { t }$ = $\pm$ 1.
C) $\Delta$ $\ell$ = 0, $\pm$ 1; $m _ { t }$ = 0, $\pm$ 1.
D) $\Delta$ $\ell$ = $\pm$ 1; $m _ { t }$ = 0, $\pm$ 1.
E) $\Delta$ $\ell$ = $\pm$ 1; $m _ { t }$ = $\pm$ 1.

Question 30

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

A) $\frac { 1 } { 2 } \hbar$
B) $\frac { \sqrt { 3 } } { 2 } \hbar$
C) $\hbar$
D)- $\hbar$
E) $- \frac { 1 } { 2 } \hbar$

Question 31

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 32

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 33

In an atom that has an electron in a sub-shell for which $\ell$ = 4,with respect to the magnetic field vector $\vec { B }$ the magnetic moment vector $\vec { \mu }$ of the electron is allowed to be oriented in

A)any direction.
B) $\ell$ discrete directions
C) $\ell$ -1 discrete directions.
D) $\ell$ + 1 discrete directions.
E)2 $\ell$ + 1 discrete directions.

Question 34

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 35

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.