Choose the incorrect statement regarding the Bohr model of the hydrogen atom

Options

A. The radius of nth orbit is proportional to `n^(2)`
B. The total energy of electron in nth orbit is proportional to n
C. The angular momentum of an electron in an orbit is an intergal multiple of `h//2pi`
D. The magnitude of the potential energy of an electron in any orbit is greater than its kinetic energy

Answer

To solve the question regarding the incorrect statement about the Bohr model of the hydrogen atom, we will analyze each option based on the key concepts of the Bohr model.

### Step-by-Step Solution:

1. **Understanding the Key Concepts**:
- The radius of the nth orbit in a hydrogen atom is given by the formula:
\[ r_n = 0.529 \times n^2 \text{ (in angstroms)} \]
- The total energy (E) of the electron in the nth orbit is given by:
\[ E_n = -\frac{13.6}{n^2} \text{ (in electron volts)} \]
- The angular momentum (L) of the electron in the nth orbit is given by:
\[ L_n = n \times \frac{h}{2\pi} \]
- The potential energy (PE) is twice the total energy:
\[ PE = 2E \]
- The kinetic energy (KE) is the negative of the total energy:
\[ KE = -E \]

2. **Analyzing Each Option**:
- **Option 1**: "The radius of the nth orbit is proportional to n square."
- This statement is correct based on the formula for radius.

- **Option 2**: "The total energy of the electron in nth orbit is proportional to n."
- This statement is incorrect. The total energy is proportional to \( \frac{1}{n^2} \), not \( n \).

- **Option 3**: "The angular momentum of the electron in an orbit is an integral multiple of \( \frac{h}{2\pi} \)."
- This statement is correct as angular momentum is defined as \( n \times \frac{h}{2\pi} \).

- **Option 4**: "The magnitude of potential energy of an electron in any orbit is greater than its kinetic energy."
- This statement is also correct because the magnitude of potential energy is indeed greater than that of kinetic energy.

3. **Conclusion**:
- After analyzing all options, we find that **Option 2** is the incorrect statement regarding the Bohr model of the hydrogen atom.

### Final Answer:
The incorrect statement regarding the Bohr model of the hydrogen atom is **Option 2**: "The total energy of the electron in nth orbit is proportional to n."