Question 1

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

Accepted Answer

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

Question 2

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?

Accepted Answer

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. 
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. B

Question 3

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

Accepted Answer

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

Question 4

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

Accepted Answer

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

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

Accepted Answer

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. 
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.

Question 6

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?

Accepted Answer

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 
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 7

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?

Accepted Answer

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

Question 8

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?

Accepted Answer

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. 
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 9

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?

Accepted Answer

(a) 3.1 x

Question 10

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

Accepted Answer

A) True 
 B)False

Question 11

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?

Accepted Answer

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

Question 12

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

Accepted Answer

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 
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 13

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?

Accepted Answer

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

Question 14

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?

Accepted Answer

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

Question 15

State Heisenberg's Uncertainty Principle.

Accepted Answer

The position and mom

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?

Accepted Answer

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. 
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

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

Accepted Answer

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

Question 18

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

Accepted Answer

It unifies the wave-particle duality int

Question 19

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.

Accepted Answer

A) True 
 B)False

Question 20

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?

Accepted Answer

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. 
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.

Exam 38: Quantum Mechanics

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

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?

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

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

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

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?

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?

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 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?

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

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?

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

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?

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?

State Heisenberg's Uncertainty Principle.

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?

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

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

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.

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?

Introduction, Measurement, Estimating

Describing Motion: Kinematics in One Dimension

Kinematics in Two or Three Dimensions; Vectors

Dynamics: Newtons Laws of Motion

Using Newtons Laws: Friction, Circular Motion, Drag Forces

Gravitation and Newtons6 Synthesis

Work and Energy

Conservation of Energy

Linear Momentum

Rotational Motion

Angular Momentum; General Rotation

Static Equilibrium; Elasticity and Fracture

Fluids

Oscillations

Wave Motion

Sound

Temperature, Thermal Expansion, and the Ideal Gas Law

Kinetic Theory of Gases

Heat and the First Law of Thermodynamics

Second Law of Thermodynamics

Electric Charge and Electric Field

Gausss Law

Electric Potential

Capacitance, Dielectrics, Electric Energy Storage

Electric Currents and Resistance

Dc Circuits

Magnetism

Sources of Magnetic Field

Electromagnetic Induction and Faradays Law

Inductance, Electromagnetic Oscillations, and Ac Circuits

Maxwells Equations and Electromagnetic Waves

Light: Reflection and Refraction

Lenses and Optical Instruments

The Wave Nature of Light; Interference

Diffraction and Polarization

Special Theory of Relativity

Early Quantum Theory and Models of the Atom

Quantum Mechanics of Atoms

Molecules and Solids

Nuclear Physics and Radioactivity

Nuclear Energy: Efects and Uses of Radiation

Elementary Particle

Astrophysics and Cosmology

Filters

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

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

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?

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?

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?