According to Bohr's theory the angular momentum of an electron in the fourth orbit is

Options

A. `(h)/(2pi)`
B. `(2h)/(pi)`
C. `(3h)/(2pi)`
D. `(3h)/(pi)`

Explanation

To find the angular momentum of an electron in the fourth orbit according to Bohr's theory, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Formula for Angular Momentum**:
According to Bohr's theory, the angular momentum (L) of an electron in an orbit is given by the formula:
\[ L = mvr = \frac{nh}{2\pi} \]
where:
- \( L \) = angular momentum
- \( n \) = principal quantum number (the orbit number)
- \( h \) = Planck's constant
- \( m \) = mass of the electron
- \( v \) = velocity of the electron
- \( r \) = radius of the orbit

2. **Identify the Principal Quantum Number**:
Since we are looking for the angular momentum of the electron in the fourth orbit, we set:
\[ n = 4 \]

3. **Substitute the Value of \( n \) into the Formula**:
Now, substitute \( n = 4 \) into the formula for angular momentum:
\[ L = \frac{nh}{2\pi} = \frac{4h}{2\pi} \]

4. **Simplify the Expression**:
Simplifying the expression gives:
\[ L = \frac{4h}{2\pi} = \frac{2h}{\pi} \]

5. **Conclusion**:
Thus, the angular momentum of the electron in the fourth orbit is:
\[ L = \frac{2h}{\pi} \]

### Final Answer:
The angular momentum of an electron in the fourth orbit according to Bohr's theory is \( \frac{2h}{\pi} \).

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