What is spin angular momentum of an electron.

Answer

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

### Step 1: Understand the formula for spin angular momentum
The formula for the spin angular momentum \( L_s \) of an electron is given by:
\[ L_s = \sqrt{s(s + 1)} \cdot \frac{h}{2\pi} \]
where:
- \( s \) is the spin quantum number,
- \( h \) is Planck's constant.

### Step 2: Identify the spin quantum number
For an electron, the spin quantum number \( s \) can take values of \( +\frac{1}{2} \) or \( -\frac{1}{2} \). However, since we are looking for the magnitude of the spin angular momentum, we will use the positive value:
\[ s = \frac{1}{2} \]

### Step 3: Substitute the value of \( s \) into the formula
Now, we substitute \( s = \frac{1}{2} \) into the formula:
\[ L_s = \sqrt{\frac{1}{2}\left(\frac{1}{2} + 1\right)} \cdot \frac{h}{2\pi} \]
This simplifies to:
\[ L_s = \sqrt{\frac{1}{2} \cdot \frac{3}{2}} \cdot \frac{h}{2\pi} \]

### Step 4: Simplify the expression
Now we simplify the expression inside the square root:
\[ L_s = \sqrt{\frac{3}{4}} \cdot \frac{h}{2\pi} \]

### Step 5: Final expression for spin angular momentum
Thus, the spin angular momentum of an electron can be expressed as:
\[ L_s = \frac{\sqrt{3}}{2} \cdot \frac{h}{2\pi} \]

### Conclusion
The spin angular momentum of an electron is given by:
\[ L_s = \frac{\sqrt{3}}{2} \cdot \frac{h}{2\pi} \]