The spin angular momentum of an electron is equal to

Options

A. `sqrt(3)`
B. `hsqrt(3)//4pi`
C. `h//2`
D. `pmh//2`

Answer

To find the spin angular momentum of an electron, we can follow these steps:

### Step 1: Understand the concept of spin angular momentum
The spin angular momentum of a particle is a fundamental property, similar to its mass or charge. For electrons, the intrinsic spin quantum number \( s \) is equal to \( \frac{1}{2} \).

### Step 2: Use the formula for spin angular momentum
The formula for the magnitude of the spin angular momentum \( L \) is given by:

\[ L = \sqrt{s(s + 1)} \hbar \]

where \( \hbar \) is the reduced Planck's constant, defined as \( \hbar = \frac{h}{2\pi} \).

### Step 3: Substitute the value of \( s \)
For an electron, we substitute \( s = \frac{1}{2} \) into the formula:

\[ L = \sqrt{\frac{1}{2} \left(\frac{1}{2} + 1\right)} \hbar \]

### Step 4: Simplify the expression
Now, simplify the expression inside the square root:

\[ L = \sqrt{\frac{1}{2} \left(\frac{3}{2}\right)} \hbar = \sqrt{\frac{3}{4}} \hbar \]

### Step 5: Finalize the expression
Thus, the spin angular momentum of an electron can be expressed as:

\[ L = \frac{\sqrt{3}}{2} \hbar \]

### Conclusion
The spin angular momentum of an electron is \( \frac{\sqrt{3}}{2} \hbar \).

---