The angular momentum of p electron is

Options

A. `(h)/(2pi)sqrt(6)`
B. `h sqrt(2)`
C. `(h)/(2pi)sqrt(2)`
D. `hsqrt(6)`

Answer

To calculate the angular momentum of a p electron, we can follow these steps:

### Step 1: Understand the formula for angular momentum
The angular momentum \( L \) of an electron in an orbital is given by the formula:
\[ L = \sqrt{l(l + 1)} \frac{h}{2\pi} \]
where \( l \) is the azimuthal quantum number and \( h \) is Planck's constant.

### Step 2: Identify the value of \( l \) for a p electron
For p electrons, the azimuthal quantum number \( l \) is equal to 1.

### Step 3: Substitute the value of \( l \) into the formula
Now, we substitute \( l = 1 \) into the angular momentum formula:
\[ L = \sqrt{1(1 + 1)} \frac{h}{2\pi} \]

### Step 4: Simplify the expression
Calculating the term inside the square root:
\[ L = \sqrt{1 \cdot 2} \frac{h}{2\pi} = \sqrt{2} \frac{h}{2\pi} \]

### Step 5: Write the final result
Thus, the angular momentum of a p electron is:
\[ L = \frac{h \sqrt{2}}{2\pi} \]

### Conclusion
The angular momentum of a p electron is \( \frac{h \sqrt{2}}{2\pi} \).

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