Chapter 11, Problem 11.42E

Physical Chemistry

2nd Edition
Ball + 3 others
ISBN: 9781133958437

Chapter
Section

Physical Chemistry

2nd Edition
Ball + 3 others
ISBN: 9781133958437
Textbook Problem

A 25-kg child is on a merry-go-round/calliope, going around and around in a large circle that has a radius of 8   meters . The child has an angular momentum of 600   kg ⋅ m 2 / s . (a) From these facts, estimate the approximate quantum number for the angular momentum the child has. (b) Estimate the quantized amount of energy the child has in this situation. How does this compare to the child’s classical energy? What principle does this illustrate?

Interpretation Introduction

(a)

Interpretation:

The approximate quantum number for the angular momentum possessed by the child on a merry-go-round is to be stated.

Concept introduction:

The wavefunction for 2-D rotational motion is given below.

Ψm=12πeimϕ

Where, Ψm represents the wavefunction dependent on quantum number m. The values of m start from 0. Also, it can take up both negative and positive values integral values.

Explanation

The formula to calculate angular momentum is given below.

L=mh2Ï€

Where,

â€¢ m is the quantum number.

â€¢ h is Planckâ€™s constant.

Rearrange the equation for m as follows.

L=mh2Ï€m=LÃ—2Ï€h

Substitute the vales in the above equation as follows.

Interpretation Introduction

(b)

Interpretation:

The quantized amount of energy possessed by the child is to be estimated. This energy is to be compared with the classical energy possessed by the child. The principle involved is to be illustrated.

Concept introduction:

The wavefunction for 2-D rotational motion is given below.

Ψm=12πeimϕ

Where, Ψm represents the wavefunction dependent on quantum number m. The values of m start from 0. Also, it can take up both negative and positive values integral values.

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