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8.6 Exercise 8

Avg difficulty 2.5

For a hydrogen atom in an excited state with principal quantum number n, show that the smallest angle that the orbital angular momentum vector can make with respect to the z-axis is θ=cos−1(n−1n).\theta = \text{cos}^{−1} \left(\sqrt{\frac{n - 1}{n}}\right) .

OpenStax University Physics Volume 3, 8.6 Lasers, exercise 8

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Adapted from University Physics Volume 3 © 2016 Rice University. Licensed under CC BY 4.0. Source: University Physics Volume 3. Imported at revision db44eb9.