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Chapter 36: Problem 7

The electron is a spin- \(\frac{1}{2}\) particle. Does this mean the electron's intrinsic angular momentum is \(\frac{1}{2} \hbar ?\) Explain.

Short Answer

Expert verified
No, the electron's intrinsic angular momentum is not \(\frac{1}{2}\hbar\) but approximately \(0.87\hbar\). This is because the formula for intrinsic angular momentum is \(\hbar \sqrt{s(s+1)}\), which takes into account not only the spin quantum number, but also the squares of it and its incremental value.

Step by step solution

01

Determine the Spin Quantum Number

Recall that the spin quantum number for electron is \(\frac{1}{2}\).
02

Use the Intrinsic Angular Momentum Formula

Apply the spin quantum number into the given formula for intrinsic angular momentum which is \(\hbar \sqrt{s(s+1)}\) . Here, \(s\) is \(\frac{1}{2}\).
03

Evaluate the Formula

When you compute \(\hbar \sqrt{s(s+1)}\), replacing \(s\) with \(\frac{1}{2}\), you obtain \(\hbar \sqrt{\frac{1}{2}(\frac{1}{2}+1)}\). This simplifies to \(\hbar \sqrt{\frac{3}{4}}\), which is approximately equal to \(0.87\hbar\).

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