The angular momentum (L) of an electron moving in a stable orbit around nucleus is

Options

A. half intergal multiple of `(h)/(2pi)`
B. integral multiple of h
C. integral multiple of`(h)/(2pi)`
D. half integral multiple of h

Answer

To solve the question regarding the angular momentum (L) of an electron moving in a stable orbit around the nucleus, we can follow these steps:

### Step 1: Understand the Concept of Angular Momentum
According to Bohr's atomic model, the angular momentum of an electron in a stable orbit is quantized. This means that it can only take on certain discrete values.

### Step 2: Recall the Formula for Angular Momentum
The formula for the angular momentum (L) of an electron in a stable orbit is given by:
\[ L = n \frac{h}{2\pi} \]
where:
- \( L \) is the angular momentum,
- \( n \) is a positive integer (1, 2, 3,...),
- \( h \) is Planck's constant.

### Step 3: Identify the Key Components
From the formula, we can see that:
- The angular momentum is directly proportional to the integer \( n \).
- The term \( \frac{h}{2\pi} \) is a constant.

### Step 4: Determine the Nature of Angular Momentum
Since \( n \) can take on integer values, the angular momentum \( L \) is an integral multiple of \( \frac{h}{2\pi} \). This means that the angular momentum can be expressed as:
\[ L = k \cdot \frac{h}{2\pi} \]
where \( k \) is an integer.

### Step 5: Choose the Correct Option
From the options provided in the question, we look for the one that states that the angular momentum is an integral multiple of \( \frac{h}{2\pi} \).

Based on our understanding, the correct option is:
- **Option 3: The angular momentum is an integral multiple of \( \frac{h}{2\pi} \)**.

### Final Answer
The angular momentum (L) of an electron moving in a stable orbit around the nucleus is an integral multiple of \( \frac{h}{2\pi} \).

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