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Chapter 8: Problem 50

What is the magnitude of the spin momentum of an electron? (Express you answer in terms of \(\hbar\) ).

Short Answer

Expert verified
The magnitude of the spin angular momentum of an electron is \(S = \frac{\sqrt{3}}{2} \hbar\).

Step by step solution

01

Identifying the spin quantum number

For an electron, the spin quantum number is \(s = \frac{1}{2}\), as it is a spin-\(\frac{1}{2}\) particle.
02

Applying the formula for the magnitude of the spin angular momentum

To find the magnitude of the spin angular momentum of an electron, plug the value of \(s\) into the formula: \[S = \sqrt{s(s+1)} \hbar\] So we have: \[S = \sqrt{\frac{1}{2}\left(\frac{1}{2}+1\right)} \hbar\]
03

Calculating the magnitude of the spin angular momentum

Simplify the expression inside the square root and solve for \(S\): \[S = \sqrt{\frac{1}{2}\left(\frac{3}{2}\right)} \hbar\] \[S = \sqrt{\frac{3}{4}} \hbar\] Thus, the magnitude of the spin angular momentum of an electron is: \[S = \frac{\sqrt{3}}{2} \hbar\]

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