In Bohr's model of the hydrogen atom, the pairs of quantities that are quantized among the following is

Options

A. Energy and linear momentum
B. Angular and linear momentum
C. Energy and angular momentum
D. None of these

Answer

To solve the question regarding the quantization of pairs of quantities in Bohr's model of the hydrogen atom, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Bohr's Model**:
- In Bohr's model, electrons revolve in specific orbits around the nucleus. The key aspect of this model is that certain physical quantities are quantized.

2. **Identifying Quantized Quantities**:
- The two primary quantities that are quantized in Bohr's model are:
- **Angular Momentum (L)**: According to Bohr's theory, the angular momentum of an electron in a hydrogen atom is quantized and given by the formula:
\[ L = n \frac{h}{2\pi} \]
where \( n \) is a positive integer (1, 2, 3, ...), and \( h \) is Planck's constant.
- **Energy (E)**: The energy of an electron in the nth orbit is also quantized and is given by:
\[ E = -\frac{13.6 \, \text{eV}}{n^2} \]
where \( n \) is again a positive integer.

3. **Conclusion**:
- Both angular momentum and energy are quantized in Bohr's model of the hydrogen atom. Therefore, the correct pair of quantized quantities is:
- **Angular Momentum and Energy**.

4. **Selecting the Correct Option**:
- Based on the analysis, the correct option is **C: Energy and Angular Momentum**.