Question 1

The ground state energy of a harmonic oscillator is:

Accepted Answer

A)    
B)    
C)    
D) E = 0 
E)    
A)    
B)    
C)    
D) E = 0 
E)

Question 2

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 3

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 $\Psi$II =

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 4

Frank says that quantum mechanics does not apply to cricket balls because they do not jump from quantum state to quantum state when being thrown.Francine agrees with him.She says that there is no uncertainty in a cricket ball's position or momentum.Are they correct, or not, and why?

Accepted Answer

A) They are correct because the first excited state of a cricket ball is at a higher energy that any cricket ball ever receives.Therefore we cannot determine whether or not there is uncertainty in its position or momentum. 
B) They are correct because the first excited state of a cricket ball is at a higher energy that any cricket ball ever receives.Therefore its position and momentum are completely uncertain until it is caught. 
C) They are wrong because the cricket ball goes through so many quantum states in being thrown that we cannot observe the transitions.The uncertainties in its position and momentum are too small to observe. 
D) They are wrong because the cricket ball goes through so many quantum states in being thrown that we cannot observe the transitions.Because of the number of transitions its position and momentum are completely uncertain until it is caught. 
E) Quantum mechanics states that they are correct as long as they do not make any observations, but wrong as soon as they begin to make observations. 
A) They are correct because the first excited state of a cricket ball is at a higher energy that any cricket ball ever receives.Therefore we cannot determine whether or not there is uncertainty in its position or momentum. 
B) They are correct because the first excited state of a cricket ball is at a higher energy that any cricket ball ever receives.Therefore its position and momentum are completely uncertain until it is caught. 
C) They are wrong because the cricket ball goes through so many quantum states in being thrown that we cannot observe the transitions.The uncertainties in its position and momentum are too small to observe. 
D) They are wrong because the cricket ball goes through so many quantum states in being thrown that we cannot observe the transitions.Because of the number of transitions its position and momentum are completely uncertain until it is caught. 
E) Quantum mechanics states that they are correct as long as they do not make any observations, but wrong as soon as they begin to make observations.

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

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 7

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 8

When the potential energy of a system is independent of time, the wave function of the system:

Accepted Answer

A) is a constant. 
B) is directly proportional to the time. 
C) cannot be normalised. 
D) depends only on the centre of mass, , of the system.   
E) depends on the vector positions, i, of each particle in the system.   
A) is a constant. 
B) is directly proportional to the time. 
C) cannot be normalised. 
D) depends only on the centre of mass, , of the system.   
E) depends on the vector positions, i, of each particle in the system.

Question 9

An electron has been accelerated by a potential difference of 100 V.If its position is known to have an uncertainty of 1 nm, what is the percent uncertainty ($\Delta$p/p *100) of the electron's momentum?

Accepted Answer

A) 1% 
B) 2% 
C) 10% 
D) >>10% 
E) 5% 
A) 1% 
B) 2% 
C) 10% 
D) >>10% 
E) 5%

Question 10

A 15-kg mass, attached to a massless spring whose force constant is 2500 N/m, has an amplitude of 4 cm.Assuming the energy is quantised, find the quantum number of the system, n, if En = nhf.

Accepted Answer

A) 1.5 *1033 
B) 3.0 * 1033 
C) 4.5 * 1033 
D) 5.4 * 1033 
E) 1.0 * 1033 
A) 1.5 *1033 
B) 3.0 * 1033 
C) 4.5 * 1033 
D) 5.4 * 1033 
E) 1.0 * 1033

Question 11

The graph below represents a wave function $\Psi$(x) for a particle confined to -2.00 m$\le$x $\le$ +2.00 m.The value of the normalisation constant A may be:

Accepted Answer

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

Question 12

Calculate the ground state energy (in eV) for an electron in a box (an infinite well) having a width of 0.050 nm.

Accepted Answer

A) 10 
B) 75 
C) 24 
D) 150 
E) 54 
A) 10 
B) 75 
C) 24 
D) 150 
E) 54

Question 13

Because of Heisenberg's Uncertainty Principle, the velocity of a particle is known least precisely when the length of the wave packet representing the particle is:

Accepted Answer

A) 10 m. 
E) the length of a plane wave (infinite) 
A) 10 m. 
E) the length of a plane wave (infinite)

Question 14

A baseball (1 kg) has an energy of 100 joules.If its uncertainty in position is 1 m, what is the percentage uncertainty ($\Delta$p/p * 100) in the momentum of the baseball?

Accepted Answer

A) <<1% 
B) 1% 
C) 2% 
D) 5% 
E) 10% 
A) <<1% 
B) 1% 
C) 2% 
D) 5% 
E) 10%

Question 15

Classically, the concept of 'tunneling' is impossible.Why?

Accepted Answer

A) The kinetic energy of the particle would be negative. 
B) The velocity of the particle would be negative. 
C) The total energy of a particle is equal to the kinetic and potential energies. 
D) The kinetic energy must be equal to the potential energy. 
E) The total energy for the particle would be negative. 
A) The kinetic energy of the particle would be negative. 
B) The velocity of the particle would be negative. 
C) The total energy of a particle is equal to the kinetic and potential energies. 
D) The kinetic energy must be equal to the potential energy. 
E) The total energy for the particle would be negative.

Question 16

The average position, or expectation value, of a particle whose wave function $\Psi$(x) depends only on the value of x, is given by  =

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 17

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 18

The wave function for a particle confined to a one-dimensional box located between x = 0 and x = L is given by $\Psi$(x) = A sin (n $\pi$x/L) + B cos (n $\pi$x/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 19

The graph below represents a wave function $\Psi$(x) for a particle confined to -4.00 m $\le$ x $\le$ +4.00 m.The magnitude of the normalisation constant A is:

Accepted Answer

A)    
B)    
C)    
D)    
E) 4. 
A)    
B)    
C)    
D)    
E) 4.

Question 20

Quantum tunnelling occurs in:

Accepted Answer

A) nuclear fusion. 
B) radioactive decay by emission of alpha particles. 
C) the scanning tunnelling microscope. 
D) nuclear fusion, radioactive decay and in the scanning tunnelling microscope. 
E) radioactive decay and the scanning tunnelling microscope only. 
A) nuclear fusion. 
B) radioactive decay by emission of alpha particles. 
C) the scanning tunnelling microscope. 
D) nuclear fusion, radioactive decay and in the scanning tunnelling microscope. 
E) radioactive decay and the scanning tunnelling microscope only.

The ground state energy of a harmonic oscillator is:

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?

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

Frank says that quantum mechanics does not apply to cricket balls because they do not jump from quantum state to quantum state when being thrown.Francine agrees with him.She says that there is no uncertainty in a cricket ball's position or momentum.Are they correct, or not, and why?

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)?

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

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?

When the potential energy of a system is independent of time, the wave function of the system:

An electron has been accelerated by a potential difference of 100 V.If its position is known to have an uncertainty of 1 nm, what is the percent uncertainty ( $\Delta$ p/p *100) of the electron's momentum?

A 15-kg mass, attached to a massless spring whose force constant is 2500 N/m, has an amplitude of 4 cm.Assuming the energy is quantised, find the quantum number of the system, n, if En = nhf.

Calculate the ground state energy (in eV) for an electron in a box (an infinite well) having a width of 0.050 nm.

Because of Heisenberg's Uncertainty Principle, the velocity of a particle is known least precisely when the length of the wave packet representing the particle is:

A baseball (1 kg) has an energy of 100 joules.If its uncertainty in position is 1 m, what is the percentage uncertainty ( $\Delta$ p/p * 100) in the momentum of the baseball?

Classically, the concept of 'tunneling' is impossible.Why?

The average position, or expectation value, of a particle whose wave function $\Psi$ (x) depends only on the value of x, is given by < 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 wave function for a particle confined to a one-dimensional box located between x = 0 and x = L is given by $\Psi$ (x) = A sin (n $\pi$ x/L) + B cos (n $\pi$ x/L) .The constants A and B are determined to be:

Quantum tunnelling occurs in:

Electric Fields

Gausss Law

Electric Potential

Energy and Capacitance

Current and Resistance

Direct-Current Circuits

Magnetic Fields

Magnetic Forces

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 Polarisation

Quantisation and Wave-Particle Duality

Atomic Physics

Quantum Physics of Molecules and Solids

Nuclei and Radioactivity

Particle Physics

Filters

Exam 18: Introduction to Quantum Mechanics

The ground state energy of a harmonic oscillator is:

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?

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\PsiΨ II =

Frank says that quantum mechanics does not apply to cricket balls because they do not jump from quantum state to quantum state when being thrown.Francine agrees with him.She says that there is no uncertainty in a cricket ball's position or momentum.Are they correct, or not, and why?

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)?

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

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?

When the potential energy of a system is independent of time, the wave function of the system:

An electron has been accelerated by a potential difference of 100 V.If its position is known to have an uncertainty of 1 nm, what is the percent uncertainty ( Δ\DeltaΔ p/p *100) of the electron's momentum?

A 15-kg mass, attached to a massless spring whose force constant is 2500 N/m, has an amplitude of 4 cm.Assuming the energy is quantised, find the quantum number of the system, n, if En = nhf.

The graph below represents a wave function Ψ\PsiΨ (x) for a particle confined to -2.00 m ≤\le≤ x ≤\le≤ +2.00 m.The value of the normalisation constant A may be:

Calculate the ground state energy (in eV) for an electron in a box (an infinite well) having a width of 0.050 nm.

Because of Heisenberg's Uncertainty Principle, the velocity of a particle is known least precisely when the length of the wave packet representing the particle is:

A baseball (1 kg) has an energy of 100 joules.If its uncertainty in position is 1 m, what is the percentage uncertainty ( Δ\DeltaΔ p/p * 100) in the momentum of the baseball?

Classically, the concept of 'tunneling' is impossible.Why?

The average position, or expectation value, of a particle whose wave function Ψ\PsiΨ (x) depends only on the value of x, is given by < 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 wave function for a particle confined to a one-dimensional box located between x = 0 and x = L is given by Ψ\PsiΨ (x) = A sin (n π\piπ x/L) + B cos (n π\piπ x/L) .The constants A and B are determined to be:

The graph below represents a wave function Ψ\PsiΨ (x) for a particle confined to -4.00 m ≤\le≤ x ≤\le≤ +4.00 m.The magnitude of the normalisation constant A is:

Quantum tunnelling occurs in:

Electric Fields

Gausss Law

Electric Potential

Energy and Capacitance

Current and Resistance

Direct-Current Circuits

Magnetic Fields

Magnetic Forces

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 Polarisation

Quantisation and Wave-Particle Duality

Atomic Physics

Quantum Physics of Molecules and Solids

Nuclei and Radioactivity

Particle Physics

Filters

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

An electron has been accelerated by a potential difference of 100 V.If its position is known to have an uncertainty of 1 nm, what is the percent uncertainty ( $\Delta$ p/p *100) of the electron's momentum?

A baseball (1 kg) has an energy of 100 joules.If its uncertainty in position is 1 m, what is the percentage uncertainty ( $\Delta$ p/p * 100) in the momentum of the baseball?

The average position, or expectation value, of a particle whose wave function $\Psi$ (x) depends only on the value of x, is given by < x > =

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