Question 1

The energy of the first excited state of a harmonic oscillator is 1500 eV.What is the energy of the ground state?

Accepted Answer

A) 500 eV 
B) 750 eV 
C) 1000 eV 
D) 250 eV 
E) 375 eV 
A) 500 eV 
B) 750 eV 
C) 1000 eV 
D) 250 eV 
E) 375 eV A

Question 2

An electron is in a harmonic oscillator potential with and energy of 692 eV.Which of the following could be valid values for the oscillator frequency $\omega$0 of the potential?

Accepted Answer

A) 5.0 * 1018 s-1 
B) 3.0 * 1017 s-1 
C) 2.7 * 1017 s-1 
D) 5.0 * 1017 s-1 
E) None are correct. 
A) 5.0 * 1018 s-1 
B) 3.0 * 1017 s-1 
C) 2.7 * 1017 s-1 
D) 5.0 * 1017 s-1 
E) None are correct. B

Question 3

What is the probability that a particle whose wave function $\Psi$(x)= A(x-2)2 for x between 0 and 1,and otherwise,$\Psi$(x)= 0,is found at x < 0.5?

Accepted Answer

A) 21.3% 
B) 26.0% 
C) 74.0% 
D) 48.6% 
E) 78.7 % 
A) 21.3% 
B) 26.0% 
C) 74.0% 
D) 48.6% 
E) 78.7 % E

Question 4

After a particle has tunneled through a potential barrier,what always happens to the wavelength of its probability wave function?

Accepted Answer

A) It increases. 
B) It decreases. 
C) It remains constant. 
D) How it changes can't be determined solely by the information given. 
A) It increases. 
B) It decreases. 
C) It remains constant. 
D) How it changes can't be determined solely by the information given.

Question 5

A beam of electrons moving in the +x direction encounters a potential barrier that is 3.42 eV high and 0.78 nm wide.Each electron has a kinetic energy of 3.41 eV and the electrons arrive at the barrier at a rate of 500 electrons/s (500 electrons every second).What is the average rate in electrons/s at which electrons pass through the barrier?

Accepted Answer

A) 435 electrons per second 
B) 282 electrons per second 
C) 225 electrons per second 
D) 176 electrons per second 
E) 65 electrons per second 
A) 435 electrons per second 
B) 282 electrons per second 
C) 225 electrons per second 
D) 176 electrons per second 
E) 65 electrons per second

Question 6

An electron is trapped in an infinite potential well.If the energy of the electron when it is in the n = 4 quantum state is 160 eV,what is the minimum possible value of the energy of the electron?

Accepted Answer

A) 5.00 eV 
B) 10.0 eV 
C) 40.0 eV 
D) 80.0 eV 
A) 5.00 eV 
B) 10.0 eV 
C) 40.0 eV 
D) 80.0 eV

Question 7

Given the complex function f(x)= (5 - 3i)+ (2 + 4i)x,what is |f(1)|2?

Accepted Answer

A) 29 
B) 40 
C) 48 
D) 50 
E) 100 
A) 29 
B) 40 
C) 48 
D) 50 
E) 100

Question 8

If a neutron of kinetic energy 5.0 MeV encounters a rectangular potential energy barrier of height 10.0 MeV and width 2.0 fm,what is the probability that the neutron will tunnel through the barrier?

Accepted Answer

A) 0.10 
B) 0.14 
C) 0.18 
D) 0.20 
E) 0.45 
A) 0.10 
B) 0.14 
C) 0.18 
D) 0.20 
E) 0.45

Question 9

In an infinite square well,for which of the following states will the particle not be found in the exact center of the well?

Accepted Answer

A) the ground state 
B) the first excited state 
C) the second excited state 
D) Any choice is correct. 
E) None are correct. 
A) the ground state 
B) the first excited state 
C) the second excited state 
D) Any choice is correct. 
E) None are correct.

Question 10

What wavelength of light does an electron confined in a rigid box of 1-nm length absorb? Assume the electron starts in the ground state.

Accepted Answer

A) 1.1 µm 
B) 0.5 µm 
C) 120 nm 
D) 8.9 µm 
A) 1.1 µm 
B) 0.5 µm 
C) 120 nm 
D) 8.9 µm

Question 11

The ground state energy of a proton in a box is 2.10 * 10-3 eV.What is the width the box?

Accepted Answer

A) 1.00 * 10-9 m. 
B) 1.00 * 10-10 m. 
C) 3.11 * 10-9 m. 
D) 6.79 * 10-9 m. 
A) 1.00 * 10-9 m. 
B) 1.00 * 10-10 m. 
C) 3.11 * 10-9 m. 
D) 6.79 * 10-9 m.

Question 12

Find the quantum number of an electron in a harmonic oscillator potential if its energy is 4900 eV and the oscillator frequency $\omega$0 is 5.0 * 1018 s-1.

Accepted Answer

A) 0 
B) 1 
C) 2 
D) 3 
E) 4 
A) 0 
B) 1 
C) 2 
D) 3 
E) 4

Question 13

An experimental measurement of the energy levels of the hydrogen molecule H2 shows that the energy levels are evenly spaced and separated by about 9 * 10-20 J.A reasonable model of one of the hydrogen atoms would then seem to be that of a hydrogen atom in a simple harmonic oscillator potential.Assuming that the hydrogen atom is attached by a spring with a spring constant k to the molecule,what is the spring constant k?

Accepted Answer

A) 2.0 N/m 
B) 700 N/m 
C) 950 N/m 
D) 1200 N/m 
E) 2600 N/m 
A) 2.0 N/m 
B) 700 N/m 
C) 950 N/m 
D) 1200 N/m 
E) 2600 N/m

Question 14

An electron is trapped in an infinite potential well.How does the amplitude of its probability wave function change as the width of the well increases?

Accepted Answer

A) It increases also. 
B) It decreases. 
C) It remains constant. 
D) How it changes can't be determined solely by the information given. 
A) It increases also. 
B) It decreases. 
C) It remains constant. 
D) How it changes can't be determined solely by the information given.

Question 15

An electron is trapped in an infinite potential well.The minimum value of its energy is 5.00 eV.What is the quantum state of the electron if its energy is 20.0 eV?

Accepted Answer

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

Question 16

When a particle moves from a region where its potential energy is zero to a region where its potential energy is greater than zero,what always happens to the wavelength of its probability wave function?

Accepted Answer

A) It increases. 
B) It decreases. 
C) It remains constant. 
D) How it changes can't be determined solely by the information given. 
A) It increases. 
B) It decreases. 
C) It remains constant. 
D) How it changes can't be determined solely by the information given.

Question 17

The wave function representing a particle's position is g(x)= 17i - (8-7i)x.At what value of x is the probability distribution function minimum?

Accepted Answer

A) 1.05 m 
B) -1.05 m 
C) 7.93 m 
D) -7.93 m 
E) 2.11 m 
A) 1.05 m 
B) -1.05 m 
C) 7.93 m 
D) -7.93 m 
E) 2.11 m

Question 18

The ground state energy of a particle in a box of width 1.0 * 10-9 m is 2.10 * 10-3 eV.What is the mass of the particle?

Accepted Answer

A) 1.62 * 10-28 kg 
B) 2.42 * 10-27 kg 
C) 6.83 * 10-27 kg 
D) 1.67 * 10-27 kg 
A) 1.62 * 10-28 kg 
B) 2.42 * 10-27 kg 
C) 6.83 * 10-27 kg 
D) 1.67 * 10-27 kg

Question 19

A surface is examined using a scanning tunneling microscope (STM).For the range of the working gap,L,between the tip and the sample surface,assume that the electron wave function for the atoms under investigation falls off exponentially as   .The tunneling current through the STM tip is proportional to the tunneling probability.In this situation,the ratio of the current when the STM tip is 0.410 nm above a surface feature to the current when the tip is at an unknown distance above the surface is 1.37.The unknown distance is

Accepted Answer

A) 0.405 nm. 
B) 0.412 nm. 
C) 0.423 nm. 
D) 0.438 nm. 
E) 0.450 nm. 
A) 0.405 nm. 
B) 0.412 nm. 
C) 0.423 nm. 
D) 0.438 nm. 
E) 0.450 nm.

Question 20

In a scanning tunneling microscope the probability of an electron from the probe to tunnel through a 0.1-nm gap is 0.1%.Calculate the work function of the probe of the scanning tunneling microscope.

Accepted Answer

A) 3.8 eV 
B) 38 eV 
C) 5.6 eV 
D) 12 eV 
E) 45 eV 
A) 3.8 eV 
B) 38 eV 
C) 5.6 eV 
D) 12 eV 
E) 45 eV

Exam 37: Quantum Mechanics

The energy of the first excited state of a harmonic oscillator is 1500 eV.What is the energy of the ground state?

An electron is in a harmonic oscillator potential with and energy of 692 eV.Which of the following could be valid values for the oscillator frequency ω\omegaω 0 of the potential?

What is the probability that a particle whose wave function Ψ\PsiΨ (x)= A(x-2)2 for x between 0 and 1,and otherwise, Ψ\PsiΨ (x)= 0,is found at x < 0.5?

After a particle has tunneled through a potential barrier,what always happens to the wavelength of its probability wave function?

An electron is trapped in an infinite potential well.If the energy of the electron when it is in the n = 4 quantum state is 160 eV,what is the minimum possible value of the energy of the electron?

Given the complex function f(x)= (5 - 3i)+ (2 + 4i)x,what is |f(1)|2?

If a neutron of kinetic energy 5.0 MeV encounters a rectangular potential energy barrier of height 10.0 MeV and width 2.0 fm,what is the probability that the neutron will tunnel through the barrier?

In an infinite square well,for which of the following states will the particle not be found in the exact center of the well?

What wavelength of light does an electron confined in a rigid box of 1-nm length absorb? Assume the electron starts in the ground state.

The ground state energy of a proton in a box is 2.10 * 10-3 eV.What is the width the box?

Find the quantum number of an electron in a harmonic oscillator potential if its energy is 4900 eV and the oscillator frequency ω\omegaω 0 is 5.0 * 1018 s-1.

An electron is trapped in an infinite potential well.How does the amplitude of its probability wave function change as the width of the well increases?

An electron is trapped in an infinite potential well.The minimum value of its energy is 5.00 eV.What is the quantum state of the electron if its energy is 20.0 eV?

When a particle moves from a region where its potential energy is zero to a region where its potential energy is greater than zero,what always happens to the wavelength of its probability wave function?

The wave function representing a particle's position is g(x)= 17i - (8-7i)x.At what value of x is the probability distribution function minimum?

The ground state energy of a particle in a box of width 1.0 * 10-9 m is 2.10 * 10-3 eV.What is the mass of the particle?

In a scanning tunneling microscope the probability of an electron from the probe to tunnel through a 0.1-nm gap is 0.1%.Calculate the work function of the probe of the scanning tunneling microscope.

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Filters

An electron is in a harmonic oscillator potential with and energy of 692 eV.Which of the following could be valid values for the oscillator frequency $\omega$ ₀ of the potential?

What is the probability that a particle whose wave function $\Psi$ (x)= A(x-2)² for x between 0 and 1,and otherwise, $\Psi$ (x)= 0,is found at x < 0.5?

Given the complex function f(x)= (5 - 3i)+ (2 + 4i)x,what is |f(1)|²?

The ground state energy of a proton in a box is 2.10 * 10^-3 eV.What is the width the box?

Find the quantum number of an electron in a harmonic oscillator potential if its energy is 4900 eV and the oscillator frequency $\omega$ ₀ is 5.0 * 10¹⁸ s^-1.

The ground state energy of a particle in a box of width 1.0 * 10^-9 m is 2.10 * 10^-3 eV.What is the mass of the particle?