Chapter 30, Problem 59PE

### College Physics

1st Edition
Paul Peter Urone + 1 other
ISBN: 9781938168000

Chapter
Section

### College Physics

1st Edition
Paul Peter Urone + 1 other
ISBN: 9781938168000
Textbook Problem

# Integrated ConceptsFind the value of l , the orbital angular momentum quantum number, for the moon around the earth. The extremely large value obtained implies that it is impossible to tell the difference between adjacent quantized orbits for macroscopic objects.

To determine

The value of l , the orbital angular momentum quantum number, for the moon around the earth.

Explanation

Given Data:

Given that there is an Earth and its moon

Formula Used:

The angular momentum is given as

â€ƒâ€ƒL=l(l+1)h2Ï€

Where l= Orbital angular momentum quantum number

â€ƒâ€ƒh= Planck's Constant

Also, the velocity of moon, during its movement around the Earth is calculated as

â€ƒâ€ƒv=2Ï€RT

Where R= Distance of center of moon from center of Earth

â€ƒâ€ƒT= Time Period of Moon's revolution

Calculation:

Angular momentum of moon is calculated as

â€ƒâ€ƒL=mRv

Substituting v=2Ï€RT in above, we get

â€ƒâ€ƒL=mR2Ï€RT

â€ƒâ€ƒL=2Ï€mR2T

Also, we know L=l(l+1)h2Ï€

Equating the above two equation, we get

â€ƒâ€ƒ2Ï€mR2T=l(l+1)h2Ï€

Also, the value of l would be very large

Thus, we have

â€ƒâ€ƒ

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