Question 1

Determine the lowest energies of a wave function of an electron in a box of width 1.0 * 10-9 m.

Accepted Answer

A) 0.080 eV 
B) 0.27 eV 
C) 0.38 eV 
D) 0.40 eV 
A) 0.080 eV 
B) 0.27 eV 
C) 0.38 eV 
D) 0.40 eV

Question 2

A quantum well device is designed to trap electrons in a 1 nm wide region.Assuming that such a device acts as a one dimensional box,what wavelength of light would these electrons absorb in making a transition from the first quantum state to the third quantum state?

Accepted Answer

A) 350 nm 
B) 399 nm 
C) 550 nm 
D) 633 nm 
A) 350 nm 
B) 399 nm 
C) 550 nm 
D) 633 nm

Question 3

An electron is placed into an infinite square well.Which statement concerning the expectation value of the position and the probability function,$\Pi$(x),is true?

Accepted Answer

A) The expectation value for the position always occurs where the probability function is a maximum. 
B) The expectation value for the position always occurs where the probability function is a minimum. 
C) The expectation value for the position always occurs where the probability function is zero. 
D) The expectation value for the position is equal to the probability function divided by the width of the well. 
E) None are true. 
A) The expectation value for the position always occurs where the probability function is a maximum. 
B) The expectation value for the position always occurs where the probability function is a minimum. 
C) The expectation value for the position always occurs where the probability function is zero. 
D) The expectation value for the position is equal to the probability function divided by the width of the well. 
E) None are true.

Question 4

An electron is confined in a one-dimensional infinite potential well of 1.0 nm.If the electron undergoes a transition from quantum state n = 2 to n = 1,what is the wavelength of light emitted by this radiative transition?

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 5

The energy of the ground state of a harmonic oscillator is 750 eV.What is the energy of the first excited state?

Accepted Answer

A) 750 eV 
B) 1000 eV 
C) 1500 eV 
D) 2250 eV 
E) 2500 eV 
A) 750 eV 
B) 1000 eV 
C) 1500 eV 
D) 2250 eV 
E) 2500 eV

Question 6

An electron is in an infinite square well of width a: (U(x)= $\infty$ for x  a).If the electron is in the first excited state,Y(x)= Asin(2$\pi$x/a),at what position is the probability function a maximum?

Accepted Answer

A) 0 
B) a/3 and 2a/3 
C) a/4 and 3a/4 
D) a/2 
E) a 
A) 0 
B) a/3 and 2a/3 
C) a/4 and 3a/4 
D) a/2 
E) a

Question 7

For an infinite square well of length L,what is the ratio of energy difference between the ground and first excited state for a square well of length L to that of 2 L?

Accepted Answer

A) 0.5 
B) 1 
C) 2 
D) 4 
E) 5 
A) 0.5 
B) 1 
C) 2 
D) 4 
E) 5

Question 8

An electron is trapped in an infinite potential well.The minimum value of its energy is 5.00 eV.What is its energy in the n = 4 quantum state?

Accepted Answer

A) 5.00 eV 
B) 10.0 eV 
C) 20.0 eV 
D) 80.0 eV 
A) 5.00 eV 
B) 10.0 eV 
C) 20.0 eV 
D) 80.0 eV

Question 9

Determine the ground state energy of a proton in a box of width 1.0 * 10-9 m.

Accepted Answer

A) 2.1 * 10-4 eV 
B) 2.1 * 10-3 eV 
C) 2.1 * 10-2 eV 
D) 2.1 * 10-1 eV 
A) 2.1 * 10-4 eV 
B) 2.1 * 10-3 eV 
C) 2.1 * 10-2 eV 
D) 2.1 * 10-1 eV

Question 10

The quantization of energy for a normal mass on a spring is not important because

Accepted Answer

A) Planck's constant is much bigger in this case than on the atomic scale. 
B) the level spacing is comparable to the total energy. 
C) the level spacing is very small compared to the total energy. 
D)    applies only to atoms. 
E) Heisenberg's Uncertainty Principle means that the energy is very spread out. 
A) Planck's constant is much bigger in this case than on the atomic scale. 
B) the level spacing is comparable to the total energy. 
C) the level spacing is very small compared to the total energy. 
D)    applies only to atoms. 
E) Heisenberg's Uncertainty Principle means that the energy is very spread out.

Question 11

What is the second lowest energy (the first excited state)of a proton in a box in an infinite square well of width 3.0 nm? The mass of the proton is 1.67 * 10-27kg.

Accepted Answer

A) 3.7 * 10-59 J 
B) 1.4 * 10-23 J 
C) 2.7 * 10-26 J 
D) 2.2 * 10-18 J 
E) 8.7 * 10-18 J 
A) 3.7 * 10-59 J 
B) 1.4 * 10-23 J 
C) 2.7 * 10-26 J 
D) 2.2 * 10-18 J 
E) 8.7 * 10-18 J

Question 12

What frequency 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) 3.4 * 1014 Hz 
B) 2.5 * 1014 Hz 
C) 6.0 * 1014 Hz 
D) 2.8 * 1014 Hz 
A) 3.4 * 1014 Hz 
B) 2.5 * 1014 Hz 
C) 6.0 * 1014 Hz 
D) 2.8 * 1014 Hz

Question 13

Consider making an artificial atom that mimics hydrogen by placing an electron in a one-dimensional infinitely deep potential well (instead of the Coulomb potential produced by a proton in a real hydrogen atom).What well width is required to produce an energy separation between the ground state and first excited state in the well that is the same as in hydrogen (E1st excited - Eground= 10.2 eV)?

Accepted Answer

A) 0.1 nm 
B) 0.3 nm 
C) 0.5 nm 
D) 2 nm 
E) 5 nm 
A) 0.1 nm 
B) 0.3 nm 
C) 0.5 nm 
D) 2 nm 
E) 5 nm

Question 14

An electron is in a harmonic oscillator potential well and is excited from the ground state to the n = 4 state by a photon of wavelength 350.0 nm.If the electron drops back down from the n = 4 state to the n = 2 state by emitting a photon,what wavelength would it have?

Accepted Answer

A) 700.0 nm 
B) 175.0 nm 
C) 525.0 nm 
D) 233.3 nm 
A) 700.0 nm 
B) 175.0 nm 
C) 525.0 nm 
D) 233.3 nm

Question 15

An electron in a harmonic oscillator potential well emits light of wavelength 419 nm as it jumps from one level to the next.The value of the corresponding spring constant is

Accepted Answer

A) 4.3 N/m. 
B) 9.8 N/m. 
C) 12.5 N/m. 
D) 18.4 N/m. 
A) 4.3 N/m. 
B) 9.8 N/m. 
C) 12.5 N/m. 
D) 18.4 N/m.

Question 16

Consider two potential wells.Both well have the same width L,but the first well is infinitely deep while the second well has a depth of 0.75 eV.How does the energy of an electron trapped in the ground state of the infinite potential well compare with the energy of an electron trapped in the ground state of the 0.75 eV deep potential well?

Accepted Answer

A) The electron in the infinitely deep well has a smaller energy. 
B) The electron in the infinitely deep well has a larger energy. 
C) The energies are the same. 
D) More information is required to make this comparison. 
A) The electron in the infinitely deep well has a smaller energy. 
B) The electron in the infinitely deep well has a larger energy. 
C) The energies are the same. 
D) More information is required to make this comparison.

Question 17

A neutron of kinetic energy is E = 22.4 MeV,the height of the potential energy barrier is U1 = 36.2 MeV and the width of the barrier is b - a = 8.4 fm.The kinetic energy of the neutron is increased by 20.0%.The neutron's probability of tunneling through the barrier increases by a factor of

Accepted Answer

A) 6.01. 
B) 11.5. 
C) 8.24. 
D) 12.3. 
E) 10.6. 
A) 6.01. 
B) 11.5. 
C) 8.24. 
D) 12.3. 
E) 10.6.

Question 18

A particle in an infinite square well of length L has a zero probability of being found at a point L/2.What is the lowest possible energy this particle can have?

Accepted Answer

A) h2/(2ma2) 
B) h2/(ma2) 
C) 2h2/(ma2) 
D) 3h2/(ma2) 
E) 4h2/(ma2) 
A) h2/(2ma2) 
B) h2/(ma2) 
C) 2h2/(ma2) 
D) 3h2/(ma2) 
E) 4h2/(ma2)

Question 19

What is the value of the normalization constant A if the wave function $\Psi$(x)= A(x-2)2 for x between 0 and 1,and otherwise,$\Psi$(x)= 0,is to represent a particle in 1 dimension?

Accepted Answer

A) sqrt(5/31) 
B) sqrt(5/33) 
C) sqrt(3/7) 
D) sqrt(1/3) 
E) None are correct. 
A) sqrt(5/31) 
B) sqrt(5/33) 
C) sqrt(3/7) 
D) sqrt(1/3) 
E) None are correct.

Question 20

A proton of kinetic energy 10.0 MeV encounters a rectangular potential energy barrier of height 30.0 MeV and width,   .The probability that the proton will tunnel through a barrier is 0.25.What is the width of the barrier?

Accepted Answer

A) 0.071 fm 
B) 0.71 fm 
C) 7.1 fm 
D) 71 fm 
A) 0.071 fm 
B) 0.71 fm 
C) 7.1 fm 
D) 71 fm

Exam 37: Quantum Mechanics

Determine the lowest energies of a wave function of an electron in a box of width 1.0 * 10-9 m.

A quantum well device is designed to trap electrons in a 1 nm wide region.Assuming that such a device acts as a one dimensional box,what wavelength of light would these electrons absorb in making a transition from the first quantum state to the third quantum state?

An electron is placed into an infinite square well.Which statement concerning the expectation value of the position and the probability function, Π\PiΠ (x),is true?

An electron is confined in a one-dimensional infinite potential well of 1.0 nm.If the electron undergoes a transition from quantum state n = 2 to n = 1,what is the wavelength of light emitted by this radiative transition?

The energy of the ground state of a harmonic oscillator is 750 eV.What is the energy of the first excited state?

An electron is in an infinite square well of width a: (U(x)= ∞\infty∞ for x < 0 and x > a).If the electron is in the first excited state,Y(x)= Asin(2 π\piπ x/a),at what position is the probability function a maximum?

For an infinite square well of length L,what is the ratio of energy difference between the ground and first excited state for a square well of length L to that of 2 L?

An electron is trapped in an infinite potential well.The minimum value of its energy is 5.00 eV.What is its energy in the n = 4 quantum state?

Determine the ground state energy of a proton in a box of width 1.0 * 10-9 m.

The quantization of energy for a normal mass on a spring is not important because

What is the second lowest energy (the first excited state)of a proton in a box in an infinite square well of width 3.0 nm? The mass of the proton is 1.67 * 10-27kg.

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

An electron is in a harmonic oscillator potential well and is excited from the ground state to the n = 4 state by a photon of wavelength 350.0 nm.If the electron drops back down from the n = 4 state to the n = 2 state by emitting a photon,what wavelength would it have?

An electron in a harmonic oscillator potential well emits light of wavelength 419 nm as it jumps from one level to the next.The value of the corresponding spring constant is

A neutron of kinetic energy is E = 22.4 MeV,the height of the potential energy barrier is U1 = 36.2 MeV and the width of the barrier is b - a = 8.4 fm.The kinetic energy of the neutron is increased by 20.0%.The neutron's probability of tunneling through the barrier increases by a factor of

A particle in an infinite square well of length L has a zero probability of being found at a point L/2.What is the lowest possible energy this particle can have?

What is the value of the normalization constant A if the wave function Ψ\PsiΨ (x)= A(x-2)2 for x between 0 and 1,and otherwise, Ψ\PsiΨ (x)= 0,is to represent a particle in 1 dimension?

A proton of kinetic energy 10.0 MeV encounters a rectangular potential energy barrier of height 30.0 MeV and width, .The probability that the proton will tunnel through a barrier is 0.25.What is the width of the barrier?

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Filters

Determine the lowest energies of a wave function of an electron in a box of width 1.0 * 10^-9 m.

An electron is placed into an infinite square well.Which statement concerning the expectation value of the position and the probability function, $\Pi$ (x),is true?

An electron is in an infinite square well of width a: (U(x)= $\infty$ for x < 0 and x > a).If the electron is in the first excited state,Y(x)= Asin(2 $\pi$ x/a),at what position is the probability function a maximum?

Determine the ground state energy of a proton in a box of width 1.0 * 10^-9 m.

What is the second lowest energy (the first excited state)of a proton in a box in an infinite square well of width 3.0 nm? The mass of the proton is 1.67 * 10^-27kg.

A neutron of kinetic energy is E = 22.4 MeV,the height of the potential energy barrier is U₁ = 36.2 MeV and the width of the barrier is b - a = 8.4 fm.The kinetic energy of the neutron is increased by 20.0%.The neutron's probability of tunneling through the barrier increases by a factor of

What is the value of the normalization constant A if the wave function $\Psi$ (x)= A(x-2)² for x between 0 and 1,and otherwise, $\Psi$ (x)= 0,is to represent a particle in 1 dimension?