The mangnitue of spin angular momentum of electron is givenby :

Options

A. `S=sqrt(s(s+1))(h)/(2pi)`
B. `S=s(h)/(2pi)`
C. `S=sqrt(3)/(2)xx(h)/(2pi)`
D. `S=pm(1)/(2)xx(h)/(2pi)`

Answer

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

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

### Step 2: Identify the Spin Quantum Number
For a single electron, the spin quantum number \( s \) can take the values of \( +\frac{1}{2} \) or \( -\frac{1}{2} \). We will use \( s = \frac{1}{2} \) for our calculations.

### Step 3: Substitute the Value of \( s \)
Substituting \( s = \frac{1}{2} \) into the formula:
\[ S = \sqrt{\frac{1}{2}\left(\frac{1}{2} + 1\right)} \cdot \frac{h}{2\pi} \]

### Step 4: Simplify the Expression
Now, simplify the expression inside the square root:
\[ S = \sqrt{\frac{1}{2} \cdot \frac{3}{2}} \cdot \frac{h}{2\pi} \]
\[ S = \sqrt{\frac{3}{4}} \cdot \frac{h}{2\pi} \]

### Step 5: Final Calculation
Now, we can express \( S \):
\[ S = \frac{\sqrt{3}}{2} \cdot \frac{h}{2\pi} \]
Thus, the magnitude of the spin angular momentum of an electron is:
\[ S = \frac{\sqrt{3}}{2} \cdot \frac{h}{2\pi} \]

### Conclusion
The final answer for the magnitude of the spin angular momentum of an electron is:
\[ S = \frac{\sqrt{3}}{2} \cdot \frac{h}{2\pi} \]