The angular momentum of electron can have the value (s) :

Options

A. (a) `(0.5h)/(pi)`
B. (b) `(h)/(pi)`
C. (c) `(h)/(0.5pi)`
D. (d) `(2.5h)/(2pi)`

Answer

To determine the possible values of angular momentum of an electron 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 quantized and given by the formula:
\[ L = n \frac{h}{2\pi} \]
where \( n \) is the principal quantum number (n = 1, 2, 3, ...), and \( h \) is Planck's constant.

2. **Calculate Angular Momentum for Different Values of n**:
- For \( n = 1 \):
\[ L = 1 \cdot \frac{h}{2\pi} = \frac{h}{2\pi} \]
- For \( n = 2 \):
\[ L = 2 \cdot \frac{h}{2\pi} = \frac{h}{\pi} \]
- For \( n = 3 \):
\[ L = 3 \cdot \frac{h}{2\pi} = \frac{3h}{2\pi} \]
- For \( n = 4 \):
\[ L = 4 \cdot \frac{h}{2\pi} = \frac{2h}{\pi} \]
- For \( n = 5 \):
\[ L = 5 \cdot \frac{h}{2\pi} = \frac{5h}{2\pi} \]

3. **Identify Possible Values**:
From the calculations above, the possible values of angular momentum for the first few principal quantum numbers are:
- \( \frac{h}{2\pi} \) (for n = 1)
- \( \frac{h}{\pi} \) (for n = 2)
- \( \frac{3h}{2\pi} \) (for n = 3)
- \( \frac{2h}{\pi} \) (for n = 4)
- \( \frac{5h}{2\pi} \) (for n = 5)

4. **Analyzing the Given Options**:
Now we will check the given options:
- Option A: \( \frac{h}{2\pi} \) (possible for n = 1)
- Option B: \( \frac{h}{\pi} \) (possible for n = 2)
- Option C: \( \frac{3h}{2\pi} \) (possible for n = 3)
- Option D: \( \frac{5h}{4\pi} \) (not possible, as it does not correspond to any integer n)

5. **Conclusion**:
The possible values of angular momentum for the electron are:
- A: \( \frac{h}{2\pi} \)
- B: \( \frac{h}{\pi} \)
- C: \( \frac{3h}{2\pi} \)

### Final Answer:
The angular momentum of an electron can have the values corresponding to options A, B, and C.

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