The angular momentum of an electron in a hydrogen atom is proportional to

Options

A. `n`
B. `n^(2)`
C. `n^(3)`
D. `sqrtn`

Answer

To solve the question regarding the angular momentum of an electron in a hydrogen atom, we will use Bohr's quantization condition. Here are the steps to derive the relationship:

### Step-by-Step Solution:

1. **Understand Bohr's Model**: According to Bohr's model of the hydrogen atom, the electron moves in circular orbits around the nucleus. The angular momentum (L) of the electron in these orbits is quantized.

2. **Bohr's Quantization Condition**: The angular momentum of the electron is given by the formula:
\[ L = mvr = n \frac{h}{2\pi} \]
where:
- \( L \) is the angular momentum,
- \( m \) is the mass of the electron,
- \( v \) is the velocity of the electron,
- \( r \) is the radius of the orbit,
- \( n \) is the principal quantum number (n = 1, 2, 3,...),
- \( h \) is Planck's constant.

3. **Identify the Proportionality**: From the equation \( L = n \frac{h}{2\pi} \), we can see that the angular momentum \( L \) is directly proportional to the principal quantum number \( n \):
\[ L \propto n \]

4. **Conclusion**: Therefore, the angular momentum of an electron in a hydrogen atom is proportional to the principal quantum number \( n \).

### Final Answer:
The angular momentum of an electron in a hydrogen atom is proportional to \( n \).