Deck 38: Quantum Mechanics

Question 1

What effect does the size of the box have on the ground state energy of a particle trapped in that box?

A)If the box is smaller, the energy is greater.
B)If the box is larger, the energy is greater.
C)The size of the box has no influence on the energy.
D)Not enough information is given to answer this question.

Answer 1

If the box is smaller, the energy is greater.

Question 2

If the accuracy in measuring the velocity of a particle increases, the accuracy in measuring its position will

A)increase.
B)decrease.
C)remain the same.
D)be uncertain.

Answer 2

decrease.

Question 3

State Heisenberg's Uncertainty Principle.

Answer 3

The position and momentum of a particle cannot both be measured precisely at the same time.

Question 4

Discuss why the new theory, called quantum mechanics, was so successful.

Question 5

In quantum tunneling, electrons and other quantum particles can tunnel through a region of space that would be forbidden to them if they were classical particles.

Question 6

Discuss the limitations of the Bohr theory.

Question 7

For objects the size of baseballs, cars, and airplanes, an uncertainty in momentum of magnitude only one percent yields a limiting uncertainty in position that

A)is also one percent.
B)is so small as to be unmeasurable.
C)is quite large.
D)does not exist.
E)is 50%.

Question 8

A particle of kinetic energy 50 eV in free space travels into a region with a potential well of depth 40 eV. What happens to its speed?

A)It remains the same.
B)It increases in the region of the well.
C)It decreases in the region of the well.
D)It cannot be determined from the information given.

Question 9

The square of the wave function represents the

A)position of the particle.
B)velocity of the particle.
C)probability of finding the particle.
D)position of the particle as a function of time.
E)probability density for finding particle.

Question 10

The excited state of a certain atom is 3.2 eV ± 0.21 eV.
(a) What is the average lifetime of this state?
(b) If the excited energy doubled (6.4 eV ± 0.21 eV) how would the lifetime be affected?

Question 11

Which one of the following is the correct expression for the Heisenberg uncertainty principle?

A)Δp_y Δy ≥ h/2π
B)Δ p_y Δy ≤ h/2π
C)Δ p_y /Δy ≤ h/2π
D)Δy/Δ p_y ≥ h/2π
E)None of the other answers is correct.

Question 12

The reason the position of a particle cannot be specified with infinite precision is the

A)coherence principle.
B)exclusion principle.
C)uncertainty principle.
D)photoelectric effect.
E)principle of relativity.

Question 13

A particle trapped in a rigid box cannot have zero energy.

Question 14

In solving for the wave function for a finite potential well, which of the following is NOT required?

A)The wave function be continuous.
B)The first derivative of the wave function be continuous.
C)There always be at least one bound state.
D)The wave function be normalized.
E)All of the above are required.

Question 15

If the position of an electron is measured very precisely there is an uncertainty in measuring its

A)kinetic energy.
B)momentum.
C)potential energy.
D)thermal energy.
E)None of the other answers is correct.

Question 16

A particle of kinetic energy 50 eV in free space travels into a region with a potential well of depth 40 eV. What happens to its wavelength?

A)It remains the same.
B)It increases in the region of the well.
C)It decreases in the region of the well.
D)It cannot be determined from the information given.

Question 17

Suppose that a particle is trapped in a box. How does the spacing in energy between adjacent energy levels change as the quantum number identifying a level increases?

A)The spacing decreases.
B)The spacing alternately increases and decreases, depending on whether the wave function is a sine or a cosine function.
C)The spacing remains constant.
D)The spacing increases.

Question 18

If the accuracy in measuring the position of a particle increases, the accuracy in measuring its velocity will

A)increase.
B)decrease.
C)remain the same.
D)be uncertain.

Question 19

A free electron has a wave function Ψ = A cos (2.0 x 10⁸ x).
(a) What is the electron's wavelength?
(b) What is the electron's kinetic energy?

Question 20

An electron has a 2% probability of tunneling through a rectangular potential barrier. If this same energy electron impinged upon another barrier of the same height but twice the thickness, what would be its probability of tunneling?

A)4%
B)2%
C)1%
D)0.04%
E)0.004%

Question 21

Assume a proton in a 1-dim box of width 3.0 fm is in its 1 st excited state.
(a) What is its "kinetic" energy (in eV)?
(b) How close (fm) to the wall of the "box" is the probability density a maximum?

Question 22

If the ground state energy level of a proton in a rigid box is 5.0 MeV, what is the width of the box?

A)2.7 × 10^-13m
B)6.4 × 10^-15m
C)2.7 × 10^-15m
D)6.4 × 10^-14m
E)6.4 × 10^-13m

Question 23

The radius of a typical nucleus is about 5.0 × 10^-15 m. Assuming this to be the uncertainty in the position of a proton in the nucleus, estimate the uncertainty in the proton's energy (in eV).

A)0.2 MeV
B)0.4 MeV
C)0.6 MeV
D)0.8 MeV
E)1.0 MeV

Question 24

If the ground state energy level of an electron in a rigid box is 5.0 eV, what is the width of the box?

A)2.3 × 10^-11 m
B)7.3 × 10^-20 m
C)2.7 × 10^-10 m
D)1.0 × 10^-10 m
E)9.1 × 10^-21 m

Question 25

If the wave function for a free electron is given by Ψ = A sin kx + B cos kx, and the electron has a speed of 5.2 x 10⁶ m/s, what is the value for k?

A)1.9 x 10^-7 m^-1 m^-1
B)1.2 x 10^-6 m^-1
C)7.2 x 10⁹ m^-1
D)4.5 x 10¹⁰ m^-1
E)3.8 x 10¹¹ m^-1

Question 26

Suppose that the speed of an electron traveling 2000 m/s is known to an accuracy of 1 part in 10⁵ (i.e., within 0.001%). What is the greatest possible accuracy within which we can determine the position of this electron?

A)2.9 mm
B)5.8 mm
C)8.7 mm
D)1.2 cm
E)1.6 cm

Question 27

A particle in a rigid box has a ground state energy of 4 MeV. What is the least energy this system can absorb?

A)16 MeV
B)4 MeV
C)25 MeV
D)12 MeV
E)8 MeV

Question 28

An electron is known to be confined to a region of width 0.1 nm. What is an approximate expression for the least kinetic energy it could have, in eV?

A)1.2 eV
B)2.7 eV
C)3.2 eV
D)3.8 eV
E)4.3 eV

Question 29

If 0.025 eV neutrons were fired through a double slit so that the first order interference occurred at 10°, what is the slit spacing?

A)2.5 × 10^-8 m
B)1.0 × 10^-9 m
C)3.1 × 10^-11 m
D)1.8 × 10^-10 m
E)No answer is correct since neutrons cannot act like waves.

Question 30

A measurement of an electron's speed is 2.0 × 10⁶ m/s and has an uncertainty of 10%. What is the minimum uncertainty in position?

A)0.29 nm
B)0.58 nm
C)0.87 nm
D)1.2 nm
E)1.6 nm

Question 31

If a particle in a rigid box has a ground state energy of 1 eV, how much higher in energy is the next state?

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

Question 32

The energy of an electron state has an uncertainty of about 0.500 eV. What is the uncertainty in the lifetime of the level?

A)1.32 × 10^-15 s
B)8.28 × 10^-15 s
C)1.32 × 10^-11 s
D)8.28 × 10^-11 s
E)1.32 × 10^-8 s

Question 33

The lifetime of uranium 238 is 6.0 × 10⁹ y, and that of uranium 235 is 1.0 × 10⁹ y. The present abundance of uranium 238 is 140 times the abundance of uranium 235. What was the ratio of abundances 1 billion years ago?

A)140:1
B)6:1
C)61:1
D)161:1
E)322:1

Question 34

If a particle is in a box with a ground state energy of 4 eV, what energy must be absorbed by the system to go from the n = 2 state to the n = 3 state?

A)4 eV
B)2 eV
C)20 eV
D)16 eV
E)36 eV

Question 35

The lifetime of an excited nuclear state is 10^-9 s. What is the minimum uncertainty in the energy of this state?

A)1 × 10^-9 eV
B)1 × 10^-25 eV
C)6 × 10^-25eV
D)5 × 10^-9 eV
E)7 × 10^-7 eV

Question 36

A certain particle's energy is known within 10^-18 J. What is the minimum uncertainty in its arrival time at a detector?

A)10^-15 s
B)10^-14 s
C)10^-13 s
D)10^-12s
E)10^-16 s

Question 37

An electron inside a hydrogen atom is confined to within a space of about 0.110 nm. If the electron mass is 9.11 x 10^-31 kg, what is the uncertainty in the electron's velocity?

A)1.05 × 10⁶ m/s
B)1.50 × 10⁶ m/s
C)1.05 × 10⁸ m/s
D)1.50 × 10⁸ m/s
E)1.05 × 10¹⁰ m/s

Question 38

The width of a nuclear state is found to be 10^-2 eV. The corresponding lifetime of this state is

A)10^-36 s.
B)10^-2 s.
C)10^-4 s.
D)4 × 10^-13 s.
E)7 × 10^-14 s.

Question 39

If the wave function for a free electron is given by Ψ = A sin kx + B cos kx, and the electron has a kinetic energy of 9.0 eV, what is the value for k?

A)2.5 x 10⁹ m^-1
B)1.0 x 10¹⁰ m^-1
C)1.5 x 10¹⁰ m^-1
D)4.5 x 10¹⁶ m^-1
E)9.7 x 10¹⁷ m^-1

Question 40

An electron (mass = 9.1 × 10^-31 kg) is confined in a cubical box 2.3 × 10^-12 m on each side. The minimum energy of the electron is approximately

A)1.1 × 10^-12 J.
B)1.1 × 10^-13 J.
C)1.1 × 10^-14 J.
D)1.1 × 10^-11 J.
E)1.1 × 10^-15 J.

Question 41

An electron in a rigid box is in the ground state. The system absorbs a 9-eV photon putting the electron in the n = 2 state. What is the width of the box?

A)1.8 × 10^-10 m
B)1.5 × 10^-10 m
C)2.5 × 10^-10 m
D)2.0 × 10^-10 m
E)3.5 × 10^-10 m

Question 42

An 80 eV electron impinges upon a potential barrier 100 eV high and 0.2 nm thick. What is the probability the electron will tunnel through the barrier?

A)10%
B)1.0%
C)0.10%
D)1.1 x 10^-4 %
E)7.7 x 10^-10 %