   Chapter 30, Problem 59PE

Chapter
Section
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

L=l(l+1)h2π

Where l= Orbital angular momentum quantum number

h= Planck's Constant

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

v=2πRT

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

T= Time Period of Moon's revolution

Calculation:

Angular momentum of moon is calculated as

L=mRv

Substituting v=2πRT in above, we get

L=mR2πRT

L=2πmR2T

Also, we know L=l(l+1)h2π

Equating the above two equation, we get

2πmR2T=l(l+1)h2π

Also, the value of l would be very large

Thus, we have

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