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Chapter 41: Q. 26 (page 1207)

a. Draw a diagram similar to Figure 41.2 to show all the possible orientations of the angular momentum vector L→for the case l=3. Label each L→with the appropriate value of m.

b. What is the minimum angle between L→and the z-axis?

Short Answer

Expert verified

Part (a) The diagram is

Part (b) the minimum angle between L→andz-axis is30°

Step by step solution

01

Step 1. Given information

(a) The number of mvalues for a particular value of lis given by the following equation2l+1

For l=3the values formare:-3,-2,-1,0,1,2,3

The diagram showing all possible orientations of angular momentum vector for the case of l=3along with the appropriate mvalues for each orientation is given below:

02

Step 2. (b) The angle between the vector L→ and z-axis is

θlm=cos-1ml(l+1)

θ33=cos-133(3+1)

=cos-1312

=cos-1(0.87)

=30°

Thus, the minimum angle between L→andz-axis=30°

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