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Chapter 36: Problem 16

Find the maximum possible magnitude for the orbital angular momentum of an electron in the \(n=7\) state of hydrogen.

Short Answer

Expert verified
The maximum magnitude of the orbital angular momentum of an electron in the \(n=7\) state of hydrogen is \(L= \sqrt{l(l+1)}h\) where \(l=6\) and \(h\) is the Planck constant.

Step by step solution

01

Identify principal quantum number

The problem statement gives that the principal quantum number \(n=7\) for the given state of hydrogen.
02

Find the maximum azimuthal quantum number

In quantum mechanics, for a given principal quantum number n, the azimuthal quantum number l can have values from 0 to \(n-1\). So, for \(n=7\), the maximum value of l would be \(7-1=6\).
03

Compute the maximum possible magnitude for angular momentum

The maximum possible orbital angular momentum L can be computed using the formula \(L=\sqrt{l(l+1)}h\). Substituting the values \(l=6\) and \(h\) as the Planck constant, we can compute the maximum possible magnitude for the angular momentum of the electron in the given state.

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