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 $\vec{L}$ for the case $l = 3$ . Label each $\vec{L}$ with the appropriate value of $m$ .
b. What is the minimum angle between $\vec{L}$ and the z-axis?

Short Answer

Expert verified

Part (a) The diagram is

Part (b) the minimum angle between $\vec{L} and z -axis is 30 °$

Step by step solution

Step 1. Given information

(a) The number of $m$ values for a particular value of $l$ is given by the following equation $2 l + 1$

For $l = 3$ the values for $m are: - 3, - 2, - 1, 0, 1, 2, 3$

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

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

$θ_{l m} = \cos^{- 1} (\frac{m}{\sqrt{l (l + 1)}})$

$θ_{33} = \cos^{- 1} (\frac{3}{\sqrt{3 (3 + 1)}})$

$= \cos^{- 1} (\frac{3}{\sqrt{12}})$

$= \cos^{- 1} (0.87)$

$= 30 °$

Thus, the minimum angle between $\vec{L} and z - axis$ $= 30 °$

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a. Draw a diagram similar to Figure 41.2 to show all the possible orientations of the angular momentum vector $\vec{L}$ for the case $l = 3$ . Label each $\vec{L}$ with the appropriate value of $m$ .
b. What is the minimum angle between $\vec{L}$ and the z-axis?

Short Answer

Step by step solution

Step 1. Given information

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

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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

Step by step solution

Step 1. Given information

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

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

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a. Draw a diagram similar to Figure 41.2 to show all the possible orientations of the angular momentum vector $\vec{L}$ for the case $l = 3$ . Label each $\vec{L}$ with the appropriate value of $m$ .
b. What is the minimum angle between $\vec{L}$ and the z-axis?