A particle of kinetic energy E0 traveling in a region in which the potential energy is zero is then incident on a potential barrier of height U0.What is the ratio of E0/U0 so that the reflection co-efficient is 75%? (Assume E0 is much less than the rest mass energy of the particle.)

A) 1.250 B) 0.7500 C) 1.778 D) 1.005 E) 1.063 A) 1.250 B) 0.7500 C) 1.778 D) 1.005 E) 1.063

An electron of kinetic energy E0 traveling in a region in which the potential energy is zero is then incident on a finite potential barrier of height U0 (= 4E0)and width a.If the potential barrier is reduced to 2E0,by what factor will the probability of penetration of the barrier be changed?

A) B) C) D) E) None of these is correct. A) B) C) D) E) None of these is correct.

Suppose the natural frequency of oscillation for H2 is $\backsim$1012 Hz,the effective spring constant between the two H atoms is of the order

A) 10-1 N/m B) 10-3 N/m C) 10-5 N/m D) 10-7 N/m E) 10-9 N/m A) 10-1 N/m B) 10-3 N/m C) 10-5 N/m D) 10-7 N/m E) 10-9 N/m

Exam 35: Applications of the Schrodinger Equation

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An electron confined to a one-dimensional box of length L = 0.2 nm makes a transition from state n = 4 to state n = 3.The wavelength of the photon emitted is

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Question 1

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Match each of the wave function on the left for a particle in a finite square well with the corresponding probability distributions on the right,in the order (a),(b),and (c).

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Question 2

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The solution for the time-independent Schrödinger equation with the following potential function and boundary conditions is

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Question 3

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The wave function for a particle in a one-dimensional box of length L

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Question 4

Which of the following statements is true?

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Question 5

A particle of kinetic energy E₀ traveling in a region in which the potential energy is zero is then incident on a potential barrier of height U₀.What is the ratio of E₀/U₀ so that the reflection co-efficient is 75%? (Assume E₀ is much less than the rest mass energy of the particle.)

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Question 6

The time-independent Schrödinger equation is

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Question 7

The energy in the ground state of an electron confined to a one-dimensional box of length L = 0.2 nm is

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Question 8

In three dimensions,the Schrödinger equation for the infinite square-well potential

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Question 9

An electron of kinetic energy E₀ traveling in a region in which the potential energy is zero is then incident on a finite potential barrier of height U₀ (= 4E₀)and width a.If the potential barrier is reduced to 2E₀,by what factor will the probability of penetration of the barrier be changed?

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Question 10

Suppose the natural frequency of oscillation for H₂ is $\backsim$ 10¹² Hz,the effective spring constant between the two H atoms is of the order

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Question 11

The energy in the first excited state of an electron confined to a one-dimensional box of length L = 0.3 nm is

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Question 12

A proton of energy E₀ traveling in a region in which the potential energy is zero is incident on a potential barrier of height U₀ = 0.5E₀.The probability that the proton will be transmitted is

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Question 13

The quantum phenomenon known as the "tunnel effect" refers to

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Question 14

You put 5 non-interacting identical fermions each of mass m into a 1-d box of dimension L.You then put 10 non-interacting bosons each of mass m into a 1-d box of length 2L.Which system has the lowest ground-state energy and what is the value of the fermion system ground-state energy divided by the boson system ground-state energy?

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Question 15

The Schrödinger equation

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Question 16

The energy in the first excited state of an electron confined to a one-dimensional box of length L = 0.2 nm is

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Question 17

Particles that have antisymmetric wave functions and are described by the Pauli exclusion principle are called

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Question 18

A particle of energy E₀ traveling in a region in which the potential energy is zero is incident on a potential barrier of height U₀ = 0.3E₀.The probability that the particle will be reflected is

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Question 19

A particle of energy E₀ traveling in a region in which the potential energy is zero is incident on a potential barrier of height U₀ = 0.4E₀.The probability that the particle will be reflected is

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Question 20

Showing 1 - 20 of 42

Exam 35: Applications of the Schrodinger Equation

An electron confined to a one-dimensional box of length L = 0.2 nm makes a transition from state n = 4 to state n = 3.The wavelength of the photon emitted is

Match each of the wave function on the left for a particle in a finite square well with the corresponding probability distributions on the right,in the order (a),(b),and (c).

The solution for the time-independent Schrödinger equation with the following potential function and boundary conditions is

The wave function for a particle in a one-dimensional box of length L

Which of the following statements is true?

A particle of kinetic energy E0 traveling in a region in which the potential energy is zero is then incident on a potential barrier of height U0.What is the ratio of E0/U0 so that the reflection co-efficient is 75%? (Assume E0 is much less than the rest mass energy of the particle.)

The time-independent Schrödinger equation is

The energy in the ground state of an electron confined to a one-dimensional box of length L = 0.2 nm is

In three dimensions,the Schrödinger equation for the infinite square-well potential

An electron of kinetic energy E0 traveling in a region in which the potential energy is zero is then incident on a finite potential barrier of height U0 (= 4E0)and width a.If the potential barrier is reduced to 2E0,by what factor will the probability of penetration of the barrier be changed?

Suppose the natural frequency of oscillation for H2 is ∽\backsim∽ 1012 Hz,the effective spring constant between the two H atoms is of the order

The energy in the first excited state of an electron confined to a one-dimensional box of length L = 0.3 nm is

A proton of energy E0 traveling in a region in which the potential energy is zero is incident on a potential barrier of height U0 = 0.5E0.The probability that the proton will be transmitted is

The quantum phenomenon known as the "tunnel effect" refers to

The Schrödinger equation

The energy in the first excited state of an electron confined to a one-dimensional box of length L = 0.2 nm is

Particles that have antisymmetric wave functions and are described by the Pauli exclusion principle are called

A particle of energy E0 traveling in a region in which the potential energy is zero is incident on a potential barrier of height U0 = 0.3E0.The probability that the particle will be reflected is

A particle of energy E0 traveling in a region in which the potential energy is zero is incident on a potential barrier of height U0 = 0.4E0.The probability that the particle will be reflected is

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A particle of kinetic energy E₀ traveling in a region in which the potential energy is zero is then incident on a potential barrier of height U₀.What is the ratio of E₀/U₀ so that the reflection co-efficient is 75%? (Assume E₀ is much less than the rest mass energy of the particle.)

Suppose the natural frequency of oscillation for H₂ is $\backsim$ 10¹² Hz,the effective spring constant between the two H atoms is of the order

A proton of energy E₀ traveling in a region in which the potential energy is zero is incident on a potential barrier of height U₀ = 0.5E₀.The probability that the proton will be transmitted is

A particle of energy E₀ traveling in a region in which the potential energy is zero is incident on a potential barrier of height U₀ = 0.3E₀.The probability that the particle will be reflected is

A particle of energy E₀ traveling in a region in which the potential energy is zero is incident on a potential barrier of height U₀ = 0.4E₀.The probability that the particle will be reflected is