Question 1

What is the quantum number n of a particle of mass m confined to a one-dimensional box of length L when its energy is 2 h2/mL2?

Accepted Answer

A) 2 
B) 8 
C) 4 
D) 1 
E) 16 
A) 2 
B) 8 
C) 4 
D) 1 
E) 16

Question 2

A particle is in the ground state of a one-dimensional box of length 1.0 m.What is the minimum value of its momentum (in kg ⋅ m/s)?

Accepted Answer

A) 9.9 × 10−34 
B) 6.6 × 10−34 
C) 3.3 × 10−34 
D) 13 × 10−34 
E) cannot be solved unless mass of particle is known. 
A) 9.9 × 10−34 
B) 6.6 × 10−34 
C) 3.3 × 10−34 
D) 13 × 10−34 
E) cannot be solved unless mass of particle is known.

Question 3

The wave function for a particle in a box of length L is given by  
)If the box extends from x = 0 to x = L,What is the probability of finding the particle between x = 0.60 L and x = 0.70 L?

Accepted Answer

A) 0.10 
B) 0.20 
C) 0.25 
D) 0.05 
E) The probability is not given. 
A) 0.10 
B) 0.20 
C) 0.25 
D) 0.05 
E) The probability is not given.

Question 4

Find the kinetic energy (in terms of Planck's constant)of a baseball (m = 1 kg)confined to a one-dimensional box that is 25 cm wide if the baseball can be treated as a wave in the ground state.

Accepted Answer

A) 3 h2 
B) 2 h2 
C) h2 
D) 4h2 
E) 0.5 h2 
A) 3 h2 
B) 2 h2 
C) h2 
D) 4h2 
E) 0.5 h2

Question 5

A particle is in the first excited state of a one-dimensional box of length 1.0 m.What is the minimum value of its momentum (in kg ⋅ m/s)?

Accepted Answer

A) 3.3 × 10−34 
B) 6.6 × 10−34 
C) 9.9 × 10−34 
D) 13 × 10−34 
E) 22 × 10−34 
A) 3.3 × 10−34 
B) 6.6 × 10−34 
C) 9.9 × 10−34 
D) 13 × 10−34 
E) 22 × 10−34

Question 6

If the interaction of a particle with its environment restricts the particle to a finite region of space,the result is the quantization of ____ of the particle.

Accepted Answer

A) the momentum 
B) the energy 
C) the velocity 
D) all of the above properties 
E) only properties (a)and (b) 
A) the momentum 
B) the energy 
C) the velocity 
D) all of the above properties 
E) only properties (a)and (b)

Question 7

The graph below shows the value of the probability density |ψ(x)|2 in the region −3.00 m ≤ x ≤ +3.00 m.The value of the constant A is

Accepted Answer

A)    . 
B)    . 
C)    . 
D)    . 
E) either   or   . 
A)    . 
B)    . 
C)    . 
D)    . 
E) either   or   .

Question 8

When U(x)is infinitely large elsewhere,the wave function of a particle restricted to the region 0 < x < L where U(x)= 0,may have the form ψ(x)=

Accepted Answer

A)    . 
B)    . 
C) Aenπx / L. 
D)    . 
E)    . 
A)    . 
B)    . 
C) Aenπx / L. 
D)    . 
E)    .

Question 9

The wave function for a particle in a box of length L is given by  
)If the box extends from x = 0 to x = L,at which of the following positions is the highest probability for finding the particle?

Accepted Answer

A) x = 0.33 L 
B) x = 0.04 L 
C) x = 0.60 L 
D) Both (a)and (b). 
E) Both (b)and (c). 
A) x = 0.33 L 
B) x = 0.04 L 
C) x = 0.60 L 
D) Both (a)and (b). 
E) Both (b)and (c).

Question 10

The fact that we can only calculate probabilities for values of physical quantities in quantum measurements means that

Accepted Answer

A) radiation and matter are not described by mathematical relations between measurements. 
B) the probabilities cannot be calculated from mathematical relationships. 
C) the results of physical measurements bear no relationship to theory. 
D) the average values of a large number of measurements correspond to the calculated probabilities. 
E) the average of the values calculated in a large number of different theories corresponds to the results of a measurement. 
A) radiation and matter are not described by mathematical relations between measurements. 
B) the probabilities cannot be calculated from mathematical relationships. 
C) the results of physical measurements bear no relationship to theory. 
D) the average values of a large number of measurements correspond to the calculated probabilities. 
E) the average of the values calculated in a large number of different theories corresponds to the results of a measurement.

Question 11

The wave function for a particle confined to a one-dimensional box located between x = 0 and x = L is given by Ψ(x)= A sin (nπx/L)+ B cos (nπx/L).The constants A and B are determined to be

Accepted Answer

A)    ,0 
B)    ,   
C) 0,   
D)    ,   
E) 2/L,0 
A)    ,0 
B)    ,   
C) 0,   
D)    ,   
E) 2/L,0

Question 12

A particle in a finite potential well has energy E,as shown below.  
The wave function in region II where x > 0 has the form ψII =

Accepted Answer

A) Ae−Cx. 
B) AeCx. 
C) F sin kx. 
D) G cos kx. 
E) F sin kx + G cos kx. 
A) Ae−Cx. 
B) AeCx. 
C) F sin kx. 
D) G cos kx. 
E) F sin kx + G cos kx.

Question 13

The graph below represents a wave function ψ(x)for a particle confined to −2.00 m ≤ x ≤ +2.00 m.The value of the normalization constant A may be

Accepted Answer

A)    . 
B)    . 
C)    . 
D)    . 
E) either   or   . 
A)    . 
B)    . 
C)    . 
D)    . 
E) either   or   .

Exam 41: Quantum Mechanics

What is the quantum number n of a particle of mass m confined to a one-dimensional box of length L when its energy is 2 h2/mL2?

A particle is in the ground state of a one-dimensional box of length 1.0 m.What is the minimum value of its momentum (in kg ⋅ m/s)?

The wave function for a particle in a box of length L is given by )If the box extends from x = 0 to x = L,What is the probability of finding the particle between x = 0.60 L and x = 0.70 L?

Find the kinetic energy (in terms of Planck's constant)of a baseball (m = 1 kg)confined to a one-dimensional box that is 25 cm wide if the baseball can be treated as a wave in the ground state.

A particle is in the first excited state of a one-dimensional box of length 1.0 m.What is the minimum value of its momentum (in kg ⋅ m/s)?

If the interaction of a particle with its environment restricts the particle to a finite region of space,the result is the quantization of ____ of the particle.

The graph below shows the value of the probability density |ψ(x)|2 in the region −3.00 m ≤ x ≤ +3.00 m.The value of the constant A is

When U(x)is infinitely large elsewhere,the wave function of a particle restricted to the region 0 < x < L where U(x)= 0,may have the form ψ(x)=

The wave function for a particle in a box of length L is given by )If the box extends from x = 0 to x = L,at which of the following positions is the highest probability for finding the particle?

The fact that we can only calculate probabilities for values of physical quantities in quantum measurements means that

The wave function for a particle confined to a one-dimensional box located between x = 0 and x = L is given by Ψ(x)= A sin (nπx/L)+ B cos (nπx/L).The constants A and B are determined to be

A particle in a finite potential well has energy E,as shown below. The wave function in region II where x > 0 has the form ψII =

The graph below represents a wave function ψ(x)for a particle confined to −2.00 m ≤ x ≤ +2.00 m.The value of the normalization constant A may be

Physics and Measurement

Motion in One Dimension

Vectors

Motion in Two Dimensions

The Laws of Motion

Circular Motion and Other Applications of Newtons Laws

Energy of a System

Conservation of Energy

Linear Momentum and Collisions

Rotation of a Rigid Object About a Fixed Axis

Angular Momentum

Static Equilibrium and Elasticity

Universal Gravitation

Fluid Mechanics

Oscillatory Motion

Wave Motion

Sound Waves

Superposition and Standing Waves

Temperature

The First Law of Thermodynamics

The Kinetic Theory of Gases

Heat Engines, entropy, and the Second Law of Thermodynamics

Electric Fields

Gausss Law

Electric Potential

Capacitance and Dielectrics

Current and Resistance

Direct-Current Circuits

Magnetic Fields

Sources of the Magnetic Field

Faradays Law

Inductance

Alternating-Current Circuits

Electromagnetic Waves

The Nature of Light and the Principles of Ray Optics

Image Formation

Wave Optics

Diffraction Patterns and Polarization

Relativity

Introduction to Quantum Physics

Atomic Physics

Molecules and Solids

Nuclear Structure

Applications of Nuclear Physics

Particle Physics and Cosmology

Filters

What is the quantum number n of a particle of mass m confined to a one-dimensional box of length L when its energy is 2 h²/mL²?

The graph below shows the value of the probability density |ψ(x)|² in the region −3.00 m ≤ x ≤ +3.00 m.The value of the constant A is

A particle in a finite potential well has energy E,as shown below. The wave function in region II where x > 0 has the form ψ_II =