For a Bohr atom, angular momentum of an electron is (n = 0, 1,2 .....)

Options

A. `(n^(2)h^(2))/(4pi)`
B. `(nh^(2))/(4pi)`
C. `(sqrt(nh))/(2pi)`
D. `(nh)/(2pi)`

Explanation

To determine the angular momentum of an electron in a Bohr atom, we can follow these steps:

### Step 1: Understand the formula for angular momentum
The angular momentum (L) of an electron in a Bohr atom is given by the formula:
\[ L = mvr \]
where:
- \( m \) is the mass of the electron,
- \( v \) is the velocity of the electron,
- \( r \) is the radius of the electron's orbit.

### Step 2: Use the quantization condition
According to Bohr's model, the angular momentum of the electron is quantized and is given by:
\[ L = \frac{nh}{2\pi} \]
where:
- \( n \) is the principal quantum number (n = 1, 2, 3,...),
- \( h \) is Planck's constant (\( h = 6.626 \times 10^{-34} \) Joule seconds).

### Step 3: Identify the correct expression
From the above formula, we can see that the angular momentum of an electron in a Bohr atom is directly proportional to the principal quantum number \( n \). Therefore, the angular momentum can be expressed as:
\[ L = \frac{nh}{2\pi} \]
This indicates that the angular momentum increases with increasing \( n \).

### Step 4: Conclusion
Thus, the angular momentum of an electron in a Bohr atom is given by the expression:
\[ L = \frac{nh}{2\pi} \]
where \( n \) can take values 1, 2, 3, and so on.