Deck 16: Atoms

Question 1

The first Bohr radius, r₀, is 0.0529 nm and the corresponding energy, E₀, is 13.6 eV. The wavelength of the light emitted as a hydrogen atom undergoes a transition from state n = 4 to n = 2 is

A) 656 nm
B) 486 nm
C) 434 nm
D) 410 nm
E) None of these is correct.

Answer 1

486 nm

Question 2

The wavelength of the visible line in the hydrogen spectrum that corresponds to m = 5 in the Balmer equation is

A) 656 nm
B) 486 nm
C) 434 nm
D) 410 nm
E) None of these is correct.

Answer 2

434 nm

Question 3

The order-of-magnitude of the diameter of an atom is closest to

A) 10^-6 m
B) 10^-8 m
C) 10^-10 m
D) 10^-12 m
E) 10^-14 m

Answer 3

10^-10 m

Question 4

The constant in the Rydberg-Ritz formula is R_H = 10.96776 µm^-1. The wavelength predicted by this formula for n₁ = 5 and n₂ = 3 is

A) 656 nm
B) 486 nm
C) 434 nm
D) 410 nm
E) None of these is correct.

Question 5

The wavelength of the visible line in the hydrogen spectrum that corresponds to m = 4 in the Balmer equation is

A) 656 nm
B) 486 nm
C) 434 nm
D) 410 nm
E) None of these is correct.

Question 6

The constant in the Rydberg-Ritz formula is R_H = 10.96776 µm^-1. The wavelength predicted by this formula for n₁ = 3 and n₂ = 2 is

A) 656 nm
B) 486 nm
C) 434 nm
D) 410 nm
E) None of these is correct.

Question 7

If the potential energy of an electron in the Bohr's model is -U₀, then the kinetic energy and the total energy of the electron are, respectively,

A) U₀ and 0.5U₀
B) 0.5U₀ and -0.5U₀
C) 0.5U₀ and 0.5U₀
D) U₀ and -0.5U₀
E) 0.5U₀ and U₀

Question 8

The binding energy of hydrogen is 13.6 eV. The wavelength of the emission line corresponding to the transition from n = 4 to n = 3 is

A) 1.9 *10^-6 m
B) 8.2 * 10^-7 m
C) 5.3 * 10⁵ m
D) 3.0 * 10^-25 m
E) 1.6 * 10¹⁴ m

Question 9

The critical experiments that established the nuclear nature of atoms were performed by

A) Bohr
B) Balmer
C) Rydberg and Ritz
D) Geiger and Marsden
E) Thomson

Question 10

The order-of-magnitude of the diameter of the nucleus is closest to

A) 10^-6 m
B) 10^-8 m
C) 10^-10 m
D) 10^-12 m
E) 10^-15 m

Question 11

According to the Bohr theory, a hydrogen atom

A) does not radiate when it is in a stationary state.
B) radiates when the electron accelerates in a circular orbit.
C) remains in the ground state until it gives off a photon.
D) gives off a continuous spectrum from the K-shell.
E) has an electron in the ground state, an electron in the n = 1 state, an electron in the
N = 2 state, and so on.

Question 12

Which of the following statements is true?

A) The size of the nucleus of an atom is $\backsim$ ⁵ times smaller than the size of the atom.
B) The size of an atom is determined by the electron cloud.
C) Most of an atom is empty space.
D) The mass of an atom is determined primarily by the mass of the nucleus.
E) All of these are correct.

Question 13

In the Bohr model of the atom

A) gravitational forces play a significant role.
B) electrons do not radiate energy when they are in a stable orbit.
C) the electrons spiral into the nucleus.
D) the energy of an electron in a stable orbit is an integral multiple of h/(2 $\pi$ ).
E) None of these is correct.

Question 14

The binding energy of a hydrogen atom is inversely proportional to the square of the principal quantum number n. The binding energy of the ground level of atomic hydrogen is 13.6 eV. The binding energy of the second (n = 2) level of the hydrogen atom is

A) +13.6 eV
B) -13.6 eV
C) -3.4 eV
D) -54.8 eV
E) +3.4 eV

Question 15

The kinetic energy of an electron moving in a circular orbit of radius r about a positive charge Ze varies

A) directly with r.
B) directly with r².
C) indirectly with r.
D) indirectly with r².
E) indirectly with r^1/2.

Question 16

The first Bohr radius, r₀, is 0.0529 nm and the corresponding energy, E₀, is 13.6 eV. The wavelength of the light emitted as a hydrogen atom undergoes a transition from state n = 3 to n = 2 is

A) 656 nm
B) 486 nm
C) 434 nm
D) 410 nm
E) None of these is correct.

Question 17

When a gold foil is bombarded with alpha particles, a small fraction of the alpha particles were scattered at large angles. The large scattering angles

A) suggested that the positive charges in an atom were uniformly distributed throughout the atom.
B) were consistent with all of the negative charge of the atom being concentrated at the center of the atom.
C) suggested that the negative charges in an atom were uniformly distributed throughout the atom.
D) required that the positive charge and most of the mass of the atom be concentrated in a very small region.
E) were consistent with the idea that the atom has a neutral nucleus.

Question 18

The radius of the n = 1 orbit in the hydrogen atom is 0.053 nm. What is the radius of the n = 3 orbit of lithium, which has three protons in its nucleus?

A) 3(0.053) nm
B) 9(0.053) nm
C) 0.053 nm
D) (1/3)(0.053) nm
E) (1/9)(0.053) nm

Question 19

The radius of the n = 1 Bohr orbit in the hydrogen atom is 0.053 nm. What is the radius of the n = 5 Bohr orbit?

A) 5(0.053) nm
B) 25(0.053) nm
C) 0.053 nm
D) (1/5)(0.053) nm
E) (1/25)(0.053) nm

Question 20

J. J. Thomson's model of an atom

A) had electrons embedded in some kind of fluid that contained most of the mass of the atom.
B) held that the fluid containing most of the mass of the atom had enough positive charge to make the atom electrically neutral.
C) failed to predict the observed frequencies for any atom.
D) depended upon electric forces to produce stability.
E) All of these are correct.

Question 21

In the energy-level diagram, the line that corresponds to the longest wavelength in the Balmer series is

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

Question 22

Using Bohr's model, the speed of an electron in the first orbit is

A) 3.14 *10⁵ m/s
B) 1.09 * 10⁶ m/s
C) 1.37 * 10⁷ m/s
D) 2.19 *10⁶ m/s
E) None of these is correct.

Question 23

The radii of the Bohr orbits in atomic hydrogen are given by .
If the radius of the first Bohr orbit (n = 1) is 0.053 nm, the radius of the third Bohr orbit (n = 3) is

A) 0.16 nm
B) 0.018 nm
C) 0.48 nm
D) 0.35 nm
E) 1.3 nm

Question 24

Bohr's quantum condition on electron orbits required

A) that the angular momentum of the electron about the hydrogen nucleus equal nh/(2 $\pi$ ).
B) that no more than one electron occupy a given stationary state.
C) the electrons to spiral into the nucleus while radiating electromagnetic waves.
D) that the energies of an electron in a hydrogen atom be equal to nE_o, where E_o is a constant energy and n is an integer.
E) None of these is correct.

Question 25

What is the difference in wavelength between the longest wavelength in the Lyman series and that of the longest wavelength in the Paschen series?

A) 1754 nm
B) 1876 nm
C) 535 nm
D) 1220 nm
E) None of these is correct.

Question 26

A photon of wavelength 80 nm is absorbed by the electron in the ground-state level of the hydrogen atom. Is this enough energy to ionize the atom? If so calculate the kinetic energy of the free electron.

A) No, ionization does not occur.
B) Yes, 1.9 eV
C) Yes, 12 eV
D) Yes, 29 eV
E) Yes, 19 eV

Question 27

What is the energy difference between the transition with the longest wavelength in the Lyman series and the transition with the shortest wavelength in the Paschen series?

A) 10.2 eV
B) 8.7 eV
C) 4.9 eV
D) 11.7 eV
E) 12.1 eV

Question 28

The energy of the nth level in a one-electron atom is E_n = -13.6(Z²/n²) eV. Consider a beryllium ion with all but one of its electrons removed (a beryllium atom normally has four electrons). What is the energy of the electron when it is in the third-lowest energy state?

A) -24 eV
B) -7.6 eV
C) -1.5 eV
D) 24 eV
E) 7.6 eV

Question 29

What is the ratio of the radius of the n = 3 orbit to that of the n = 2 orbit?

A) 1.50
B) 4.50
C) 2.25
D) 0.666
E) None of these is correct.

Question 30

The above figure shows a schematic energy-level diagram for the hydrogen atom. The series that represents the Balmer series is

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

Question 31

An electron in a hydrogen atom jumps from the n = 5 to n = 3 level. Is a photon absorbed or emitted in this process? What is the wavelength of the photon? State whether the photon is in the visible, ultraviolet, or infrared range of the electro-magnetic spectrum.

A) absorbed, 1280 nm, infrared
B) emitted, 605 nm, visible
C) emitted, 1280 nm, infrared
D) absorbed, 605 nm, visible
E) emitted, 605 nm, infrared

Question 32

The energy of the nth level in a one-electron atom is E_n = -13.6(Z²/n²) eV. Consider a beryllium ion with all but one of its electrons removed (a beryllium atom normally has four electrons). What is the wavelength of a photon emitted when the electron makes the transition from the third-lowest to the lowest energy state?

A) 1.03 * 10^-7 m
B) 2.03 * 10^-8 m
C) 6.43 * 10^-9 m
D) 5.71 * 10^-9 m
E) 1.03 * 10^-27 m

Question 33

The electron in a hydrogen atom has an orbital radius of 0.0500 nm. To avoid being pulled into the nucleus by electrostatic attraction, the electron must have an orbital speed of

A) 7.12 km/s
B) 25.2 km/s
C) 1.02 *10⁶ m/s
D) 2.25 *10⁶ m/s
E) 5.0 *10⁸ m/s

Question 34

An electron undergoes a transition from n = 2 to n = 5. According to Bohr's model, the change in angular momentum of the electron is

A)
B)
C)
D)
E) None of these is correct.

Question 35

According to the Bohr theory, the allowed energy states for the hydrogen atom are given by the relation .
This formula can be readily extended to other hydrogenic (one-electron) systems. The energy of the second level (n = 2) for the doubly ionized lithium atom is

A) -54.4 eV
B) 13.6 eV
C) -30.6 eV
D) -3.4 eV
E) -1.5 eV

Question 36

The equation derived by Bohr for the wavelengths of $\lambda$ of the lines in hydrogen- like spectra is The first member of the Balmer series of hydrogen has $\lambda$ = 660 nm. Doubly ionized is hydrogen-like. The wavelength of the first member of the Balmer series for doubly ionized is

A) 73 nm
B) 5.9 * 10³ nm
C) 150 nm
D) 60 nm
E) 1.8* 10^-3 nm

Question 37

Light of wavelength 411 nm is observed from a hydrogen discharge. What transition produces this emission? The energy of the n = 1 level is -13.6 eV.

A) n = 1.13 to n =1
B) n = 6 to n = 2
C) n = 3 to n = 3
D) n = 2 to n = 6
E) n = 5 to n = 1

Question 38

What is the energy difference between the transition with the longest wavelength and the transition with the shortest wavelength in the Balmer series?

A) 10.2 eV
B) 3.4 eV
C) 1.51 eV
D) 12.1 eV
E) 0.66 eV

Question 39

According to Bohr's model, the radius of an electron at n = 4 is

A) 0.212 nm
B) 0.846 nm
C) 0.0265 nm
D) 0.00331 nm
E) None of these is correct.

Question 40

The red line in the hydrogen emission spectrum is 656 nm. If the energy of the nth level is -13.6/n ² eV, then calculate the transition between n levels that this emitted photon comes from.

A) n = 2 to n = 3
B) n = 4 to n = 3
C) n = 5 to n = 2
D) n = 3 to n = 2
E) n = 2 to n = 4

Question 41

In the Bohr Model of the hydrogen atom, what is the kinetic energy of the electron in the n = 3 orbit? (The radius of the 1st Bohr orbit is 0.0529 nm.)

A) 3.44 eV
B) 1.51 eV
C) 3.02 eV
D) 0.75 eV
E) 4.53 eV

Question 42

A hydrogen atom is in a state with principal quantum number n = 3. A possible value for its orbital angular momentum is

A) zero
B)
C)
D)
E)

Question 43

If you measure the angular momentum of an electron in units of , you find that the angular momentum is quantized to the value _______ units and that its component along any direction can have only the _______ values ranging from - to + units.

A)
B)
C)
D)
E)

Question 44

A possible value of the orbital angular momentum of an electron in the n = 2 state is

A)
B)
C)
D)
E)

Question 45

Consider a beryllium (Z = 4) ion with all but one of its electrons removed. What is the kinetic energy of the electron in the n = 1 orbit. (The radius of the 1st Bohr orbit in Be³⁺ is 0.0132 nm.)

A) 54.4 eV
B) 218 eV
C) 13.6 eV
D) 27.2 eV
E) 109 eV

Question 46

If the angular momentum is characterized by the quantum number = 3, what is the smallest possible angle between and the z axis?

A) 12.1º
B) 17.5º
C) 23.2º
D) 27.4º
E) 30.0º

Question 47

For the principal quantum number n = 4, the number of values the orbital quantum number l can have is

A) 4
B) 3
C) 7
D) 16
E) 6

Question 48

If the angular momentum is characterized by the quantum number = 3, what is the largest possible angle between and the +z axis?

A) 30.0º
B) 60.8º
C) 81.4º
D) 150º
E) 163º

Question 49

The principle quantum number of an electron is 3. The possible magnitudes of the orbital angular momentum, L, are

A)
B)
C)
D)
E) None of these is correct.

Question 50

The possible orbital quantum numbers of an electron are 0, 1, 3, 4, and 5. Its principal quantum number, n, and the largest magnetic quantum number, m_l are

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

Question 51

In the Bohr Model of the hydrogen atom, what is the potential energy of the electron in the n = 11 orbit? (The radius of the 1st Bohr orbit is 0.0529 nm.)

A) 2.25 * 10^-1 eV
B) 1.12*10^-1 eV
C) 5.62 * 10^-2 eV
D) 2.47 eV
E) None of these is correct.

Question 52

What is the magnitude of the change in potential energy for the electron in the hydrogen atom as it moves from the n = 2 to n = 3 orbit? (The radius of the 1st Bohr orbit is 0.0529 nm.)

A) 1.89 eV
B) 4.91 eV
C) 0.945 eV
D) 3.78 eV
E) None of these is correct.

Question 53

The symbol that represents the orbital quantum number is

A) n
B) m
C) L
D)
E) z

Question 54

The orbital angular momentum of an electron in a D state has a magnitude of . The figure shows orientations of the angular momentum vector or an electron placed in a magnetic field in the positive z direction. The vector that represents a correct orientation when the field is applied is

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

Question 55

In the Bohr Model of the hydrogen atom, what is the ratio of the speed of the electron moving in the n = 2 orbit divided by the speed of the electron in the n = 3 orbit?

A) 0.66
B) 1.5
C) 2.25
D) 0.44
E) its speed is independent of n

Question 56

The symbol that represents the orbital angular momentum is

A) n
B) m
C) L
D)
E) z

Question 57

If the angular momentum is characterized by the quantum number = 3, what are the possible values of L_z in units of ?

A) -3, 0, +3
B) -3, -2, -1, 0
C) -2, -1, 0, +1, +2
D) -3, -2, -1, 0, +1, +2, +3

Question 58

The symbol that represents the principal quantum number is

A) n
B) m
C) L
D)
E) z

Question 59

A hydrogen atom that has an electron with an orbital angular momentum is placed in a magnetic field oriented in the z direction. The component of L in the z direction could be

A)
B)
C)
D)
E)

Question 60

The orbital angular momentum L is related to the orbital quantum number by

A)
B)
C)
D)
E)

Question 61

For the hydrogen atom in the state n = 2, l = 0, m = 0, the radial probability density is The probability of finding the electron in the range $\Delta$ r = 0.04a₀ at r = 1.5a₀ is

A) 0.00377
B) 0.00249
C) 0.00428
D) 0.0271
E) zero

Question 62

For the hydrogen atom in the ground state, the radial probability density is The probability of finding the electron in the range $\Delta$ r = 0.04a₀ at r = 2a₀ is

A) 0.0463
B) 0.0184
C) 0.0217
D) 0.0117
E) 0.0341

Question 63

The set of quantum numbers for the probability density shown is

A) n = 2, = 0, m = 0
B) n = 2, = 0, m = 1
C) n = 2, = 1, m = 0
D) n = 1, = 0, m = 0
E) n = 1, = 1, m = 0

Question 64

For the hydrogen atom in the ground state, the wave function is The probability of finding the electron from r = 0 to r = 2a₀ is approximately
Note:

A) 6.34%
B) 12.7%
C) 18.0%
D) 32.3%
E) 76.2%

Question 65

The set of quantum numbers for the probability density shown is

A) n = 2, = 0, m = 0
B) n = 2, = 0, m = 2
C) n = 2, = 1, m= ±1
D) n = 1, = 0, m = ±2
E) n = 1, = 1, m = 0

Question 66

Use the following figure for the next two problems.
The energy of a hydrogen atom in the n = 5 state is approximately

A) -68 eV
B) -0.54 eV
C) +68 eV
D) +2.7 eV
E) +0.54 eV

Question 67

For the principal quantum number n = 4, the number of values the magnetic quantum number m can have is

A) 4
B) 3
C) 7
D) 16
E) 6

Question 68

A compact disc of a CD player has a moment of inertia I = 2.5 *10^-5 kg · m² and rotates at 500 rev/min. Taking L = I $\omega$ and using the quantization of angular momentum, the approximate value of L is ( = 1.055* 10^-34 J · s)

A) 1.2* 10³²
B) 2.0 * 10³⁰
C) 1.2* 10³¹
D) 130
E) 3.5 * 10¹⁵

Question 69

Use the following figure for the next two problems.
What is the longest wavelength needed for an electron to make the transition labeled (f)?

A) 151 nm
B) 365 nm
C) 422 nm
D) 821 nm
E) 1459 nm

Question 70

The total number of distinct electron states (including spin) when n = 5 is

A) 18
B) 22
C) 25
D) 50
E) 72

Question 71

For the hydrogen atom in the ground state, the wave function is The probability of finding the electron from r = 0 to r = a₀ is approximately
Note:

A) 6.34%
B) 12.7%
C) 18.0%
D) 32.3%
E) 76.2%

Question 72

For the hydrogen atom in the ground state, the radial probability density is The probability of finding the electron in the range $\Delta$ r = 0.04a₀ at r = a₀ is

A) 0.0423
B) 0.0164
C) 0.0217
D) 0.0137
E) 0.0241

Question 73

For the hydrogen atom in the state n = 2, l = 0, m = 0, the radial probability density is The probability of finding the electron in the range $\Delta$ r = 0.04a₀ at r = 2a₀ is

A) 0.0167
B) 0.149
C) 0.128
D) 0.0241
E) zero

Question 74

The set of quantum numbers for the probability density shown is

A) n = 2, = 0, m = 0
B) n = 2, = 1, m = 0
C) n = 2, = 1, m = 1
D) n = 2, = 0, m = 1
E) n = 1, = 1, m = 0

Question 75

The dashed curve on the graph shows the probability of finding the electron at a distance r for

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

Question 76

For the hydrogen atom in the ground state, the radial probability density is The probability of finding the electron in range $\Delta$ r = 0.08a₀ at r = 2a₀ is approximately

A) 2.34%
B) 3.67%
C) 5.86%
D) 6.25%
E) 7.43%

Question 77

The solid curve on the graph shows the probability of finding the electron at a distance r for

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

Question 78

Use the following figure for the next two problems.
Which of the following transitions from (a) to (e) is(are) not allowed?

A) (a) and (b)
B) (d) and (e)
C) (c) and (e)
D) (c)
E) (d)

Question 79

For the hydrogen atom in the ground state, the radial probability density is The probability of finding the electron in range $\Delta$ r = 0.08a₀ at r = a₀ is approximately

A) 3.24%
B) 4.33%
C) 5.87%
D) 6.25%
E) 7.43%

Question 80

An electron has a wave function given by The probability of finding the electron when $\theta$ = 90 $\degree$ and $\Delta$$\theta$ = $\pm$ 0.5 $\degree$ 10, and from r = a₀ to 1.06a₀ is approximately

A) zero
B) 2.12%
C) 4.75%
D) 5.8%
E) 6.34%