According to Bohr's theory the possible value of angular momentum of an electron orbiting in hydrogen atom is

Options

A. `(4h)/(3π)`
B. `h/π`
C. `(4h)/(5π)`
D. both (1) & (3)

Answer

To determine the possible values of angular momentum of an electron orbiting in a hydrogen atom according to Bohr's theory, we can follow these steps:

### Step 1: Understand Bohr's Postulate
According to Bohr's theory, the angular momentum (L) of an electron in a stationary orbit around the nucleus is quantized. This means it can only take specific values.

### Step 2: Write the Formula for Angular Momentum
Bohr's theory states that the angular momentum of the electron is given by the formula:
\[ L = n \frac{h}{2\pi} \]
where:
- \( L \) is the angular momentum,
- \( n \) is the principal quantum number (an integer: 1, 2, 3,...),
- \( h \) is Planck's constant.

### Step 3: Identify Possible Values of \( n \)
The principal quantum number \( n \) can take positive integer values:
- \( n = 1, 2, 3, \ldots \)

### Step 4: Calculate Angular Momentum for Different Values of \( n \)
Using the formula, we can calculate the angular momentum for the first few values of \( n \):
- For \( n = 1 \):
\[ L_1 = 1 \cdot \frac{h}{2\pi} = \frac{h}{2\pi} \]
- For \( n = 2 \):
\[ L_2 = 2 \cdot \frac{h}{2\pi} = \frac{2h}{2\pi} = \frac{h}{\pi} \]
- For \( n = 3 \):
\[ L_3 = 3 \cdot \frac{h}{2\pi} = \frac{3h}{2\pi} \]
- And so on for higher values of \( n \).

### Step 5: Conclusion
The possible values of angular momentum for an electron in a hydrogen atom according to Bohr's theory are:
\[ L = n \frac{h}{2\pi} \]
where \( n \) can take values 1, 2, 3, etc. Thus, the first few values are:
- \( \frac{h}{2\pi} \) for \( n = 1 \)
- \( \frac{h}{\pi} \) for \( n = 2 \)
- \( \frac{3h}{2\pi} \) for \( n = 3 \)