(a) Interpretation: The energy of the given 3-D rotational wavefunction is to be calculated. Concept introduction: The energy for the 3-D rotational motion is given by, E = l ( l + 1 ) ℏ 2 2 I The energy of the particle depends on the moment of inertia, quantum number and Planck’s constant. The total energy is quantized.

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Answer 1

Question

Chapter 11, Problem 11.55E

Interpretation Introduction

(a)

Interpretation:

The energy of the given 3-D rotational wavefunction is to be calculated.

Concept introduction:

The energy for the 3-D rotational motion is given by,

E=l(l+1)ℏ22I

The energy of the particle depends on the moment of inertia, quantum number and Planck’s constant. The total energy is quantized.

Interpretation Introduction

(b)

Interpretation:

Total angular momentum of the given 3-D rotational wavefunction is to be calculated.

Concept introduction:

The total angular momentum for the 3-Dimensional system is given by,

L=l(l+1)ℏ

The total angular momentum does not depend on the mass of the particle, radius of the rotation and also the magnetic quantum number.

Interpretation Introduction

(c)

Interpretation:

The z-component of the total angular momentum of the given 3-D rotational wavefunction is to be calculated.

Concept introduction:

The z-component of the three dimensional angular momentum that has components in x, y and z direction is quantized. Its value depends on the magnetic quantum number and it is given by,

L^z=mlℏ

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Students have asked these similar questions

Imagine a particle free to move in the x direction. Which of the following wavefunctions would be acceptable for such a particle? In eachcase, give your reasons for accepting or rejecting each function. (i) Ψ(x)=x2; (ii) Ψ(x)=1/x; (iii) Ψ(x)=e-x^2.

The rotation of a molecule can be represented by the motion of a particle moving over the surface of a sphere with angular momentum quantum number l = 2. Calculate the magnitude of its angular momentum and the possible components of the angular momentum along the z-axis. Express your results as multiples of ℏ.

A normalized wavefunction for a particle confined between 0 and L in the x direction is ψ = (2/L)1/2 sin(πx/L). Suppose that L = 10.0 nm. Calculate the probability that the particle is (a) between x = 4.95 nm and 5.05 nm, (b) between x = 1.95 nm and 2.05 nm, (c) between x = 9.90 nm and 10.00 nm, (d) between x = 5.00 nm and 10.00 nm.

Answer 2

Question

Chapter 11, Problem 11.55E

Interpretation Introduction

(a)

Interpretation:

The energy of the given 3-D rotational wavefunction is to be calculated.

Concept introduction:

The energy for the 3-D rotational motion is given by,

E=l(l+1)ℏ22I

The energy of the particle depends on the moment of inertia, quantum number and Planck’s constant. The total energy is quantized.

Interpretation Introduction

(b)

Interpretation:

Total angular momentum of the given 3-D rotational wavefunction is to be calculated.

Concept introduction:

The total angular momentum for the 3-Dimensional system is given by,

L=l(l+1)ℏ

The total angular momentum does not depend on the mass of the particle, radius of the rotation and also the magnetic quantum number.

Interpretation Introduction

(c)

Interpretation:

The z-component of the total angular momentum of the given 3-D rotational wavefunction is to be calculated.

Concept introduction:

The z-component of the three dimensional angular momentum that has components in x, y and z direction is quantized. Its value depends on the magnetic quantum number and it is given by,

L^z=mlℏ

Expert Solution & Answer

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Check out a sample textbook solution

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Answer 3

Question

Chapter 11, Problem 11.55E

Interpretation Introduction

(a)

Interpretation:

The energy of the given 3-D rotational wavefunction is to be calculated.

Concept introduction:

The energy for the 3-D rotational motion is given by,

E=l(l+1)ℏ22I

The energy of the particle depends on the moment of inertia, quantum number and Planck’s constant. The total energy is quantized.

Interpretation Introduction

(b)

Interpretation:

Total angular momentum of the given 3-D rotational wavefunction is to be calculated.

Concept introduction:

The total angular momentum for the 3-Dimensional system is given by,

L=l(l+1)ℏ

The total angular momentum does not depend on the mass of the particle, radius of the rotation and also the magnetic quantum number.

Interpretation Introduction

(c)

Interpretation:

The z-component of the total angular momentum of the given 3-D rotational wavefunction is to be calculated.

Concept introduction:

The z-component of the three dimensional angular momentum that has components in x, y and z direction is quantized. Its value depends on the magnetic quantum number and it is given by,

L^z=mlℏ

Expert Solution & Answer

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Answer 4

Question

Chapter 11, Problem 11.55E

Interpretation Introduction

(a)

Interpretation:

The energy of the given 3-D rotational wavefunction is to be calculated.

Concept introduction:

The energy for the 3-D rotational motion is given by,

E=l(l+1)ℏ22I

The energy of the particle depends on the moment of inertia, quantum number and Planck’s constant. The total energy is quantized.

Interpretation Introduction

(b)

Interpretation:

Total angular momentum of the given 3-D rotational wavefunction is to be calculated.

Concept introduction:

The total angular momentum for the 3-Dimensional system is given by,

L=l(l+1)ℏ

The total angular momentum does not depend on the mass of the particle, radius of the rotation and also the magnetic quantum number.

Interpretation Introduction

(c)

Interpretation:

The z-component of the total angular momentum of the given 3-D rotational wavefunction is to be calculated.

Concept introduction:

The z-component of the three dimensional angular momentum that has components in x, y and z direction is quantized. Its value depends on the magnetic quantum number and it is given by,

L^z=mlℏ

Expert Solution & Answer

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Answer 5

Chapter 11, Problem 11.55E

Interpretation Introduction

(a)

Interpretation:

The energy of the given 3-D rotational wavefunction is to be calculated.

Concept introduction:

The energy for the 3-D rotational motion is given by,

E=l(l+1)ℏ22I

The energy of the particle depends on the moment of inertia, quantum number and Planck’s constant. The total energy is quantized.

Interpretation Introduction

(b)

Interpretation:

Total angular momentum of the given 3-D rotational wavefunction is to be calculated.

Concept introduction:

The total angular momentum for the 3-Dimensional system is given by,

L=l(l+1)ℏ

The total angular momentum does not depend on the mass of the particle, radius of the rotation and also the magnetic quantum number.

Interpretation Introduction

(c)

Interpretation:

The z-component of the total angular momentum of the given 3-D rotational wavefunction is to be calculated.

Concept introduction:

The z-component of the three dimensional angular momentum that has components in x, y and z direction is quantized. Its value depends on the magnetic quantum number and it is given by,

L^z=mlℏ

Answer 6

Chapter 11, Problem 11.55E

Interpretation Introduction

(a)

Interpretation:

The energy of the given 3-D rotational wavefunction is to be calculated.

Concept introduction:

The energy for the 3-D rotational motion is given by,

E=l(l+1)ℏ22I

The energy of the particle depends on the moment of inertia, quantum number and Planck’s constant. The total energy is quantized.

Answer 7

Chapter 11, Problem 11.55E

Interpretation Introduction

(a)

Interpretation:

The energy of the given 3-D rotational wavefunction is to be calculated.

Concept introduction:

The energy for the 3-D rotational motion is given by,

E=l(l+1)ℏ22I

The energy of the particle depends on the moment of inertia, quantum number and Planck’s constant. The total energy is quantized.

Answer 8

Interpretation Introduction

(b)

Interpretation:

Total angular momentum of the given 3-D rotational wavefunction is to be calculated.

Concept introduction:

The total angular momentum for the 3-Dimensional system is given by,

L=l(l+1)ℏ

The total angular momentum does not depend on the mass of the particle, radius of the rotation and also the magnetic quantum number.

Answer 9

Interpretation Introduction

(b)

Interpretation:

Total angular momentum of the given 3-D rotational wavefunction is to be calculated.

Concept introduction:

The total angular momentum for the 3-Dimensional system is given by,

L=l(l+1)ℏ

The total angular momentum does not depend on the mass of the particle, radius of the rotation and also the magnetic quantum number.

Answer 10

Interpretation Introduction

(c)

Interpretation:

The z-component of the total angular momentum of the given 3-D rotational wavefunction is to be calculated.

Concept introduction:

The z-component of the three dimensional angular momentum that has components in x, y and z direction is quantized. Its value depends on the magnetic quantum number and it is given by,

L^z=mlℏ

Answer 11

Interpretation Introduction

(c)

Interpretation:

The z-component of the total angular momentum of the given 3-D rotational wavefunction is to be calculated.

Concept introduction:

The z-component of the three dimensional angular momentum that has components in x, y and z direction is quantized. Its value depends on the magnetic quantum number and it is given by,

L^z=mlℏ

Answer 12

Expert Solution & Answer

Answer 13

Expert Solution & Answer

Answer 14

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Answer 15

Ch. 11 - Convert 3.558mdyn/A into units of N/m.Ch. 11 - Prob. 11.2E Ch. 11 - Prob. 11.3E Ch. 11 - Prob. 11.4E Ch. 11 - Prob. 11.5E Ch. 11 - Prob. 11.6E Ch. 11 - Prob. 11.7E Ch. 11 - Prob. 11.8E Ch. 11 - Prob. 11.9E Ch. 11 - Prob. 11.10E

Solution Summary: The author explains that the energy of the 3-D rotational motion depends on the moment of inertia, quantum number, and Planck's constant.

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Chapter 11 Solutions