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 quantized 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 of the hydrogen atom, electrons revolve around the nucleus in specific orbits. Each orbit corresponds to a certain energy level.

2. **Identifying Quantized Quantities**:
- According to Bohr's theory, two key quantities are quantized:
- **Angular Momentum (L)**: The angular momentum of the electron in its orbit is quantized and is 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 the electron in the nth orbit is also quantized and is given by:
\[ E_n = -\frac{13.6 \, \text{eV}}{n^2} \]
where \( n \) is again a positive integer.

3. **Evaluating Options**:
- Now, we need to evaluate the pairs of quantities provided in the question:
- **Option 1**: Energy and Linear Momentum - Energy is quantized, but linear momentum is not quantized in the same way.
- **Option 2**: Angular Momentum and Linear Momentum - Angular momentum is quantized, but linear momentum is not quantized.
- **Option 3**: Energy and Angular Momentum - Both are quantized.
- **Option 4**: None of these - This option is incorrect since we have found a valid pair.

4. **Conclusion**:
- The correct answer is **Option 3: Energy and Angular Momentum**, as both quantities are quantized in Bohr's model of the hydrogen atom.