The minimum orbital angular momentum of the electron in a hydrogen atom is

Options

A. `h`
B. `h//2`
C. `h//2 pi`
D. `h// lambda`

Answer

To find the minimum orbital angular momentum of the electron in a hydrogen atom, we can follow these steps:

### Step 1: Understand Bohr's Model
According to Bohr's model of the atom, the angular momentum (L) of an electron in a hydrogen atom is quantized and is given by the formula:
\[ L = n \cdot \frac{h}{2\pi} \]
where:
- \( L \) is the orbital angular momentum,
- \( n \) is the principal quantum number,
- \( h \) is Planck's constant.

### Step 2: Identify the Minimum Principal Quantum Number
The principal quantum number \( n \) can take positive integer values (1, 2, 3, ...). The minimum value of \( n \) is 1.

### Step 3: Substitute the Minimum Value of \( n \)
Substituting \( n = 1 \) into the angular momentum formula:
\[ L = 1 \cdot \frac{h}{2\pi} \]
This simplifies to:
\[ L = \frac{h}{2\pi} \]

### Step 4: Conclusion
Thus, the minimum orbital angular momentum of the electron in a hydrogen atom is:
\[ L = \frac{h}{2\pi} \]

### Final Answer
The minimum orbital angular momentum of the electron in a hydrogen atom is \( \frac{h}{2\pi} \).

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