Which of the following statements is (are) wrong for hydrogen atom?

Options

A. The rotational frequency of an electron in an orbit of radius r proportional to the cube of the radius of the orbit
B. The linear momentum of the revolving electron is inversely proportional to the square root of the radius of the orbit
C. The total energy of the system is inversely proportional to the radius of the orbit
D. The magnetic moment of the electron is proportional to square of the radius of the orbit

Answer

To determine which statements about the hydrogen atom are incorrect, we will analyze each statement one by one.

### Step-by-Step Solution:

1. **Statement 1**: "The rotational frequency of an electron in an orbit of radius r is proportional to the cube of the radius of the orbit."
- **Analysis**: The frequency of an electron in a circular orbit is given by the formula \( f \propto \frac{1}{r^{3/2}} \). This means that the frequency is inversely proportional to the square root of the radius cubed, not directly proportional to the cube of the radius.
- **Conclusion**: This statement is **wrong**.

2. **Statement 2**: "The linear momentum is inversely proportional to the square root of the radius of the orbit."
- **Analysis**: The linear momentum \( p \) of the electron in an orbit is given by \( p \propto \frac{1}{\sqrt{r}} \). This means that as the radius increases, the linear momentum decreases, which supports the statement.
- **Conclusion**: This statement is **correct**.

3. **Statement 3**: "The total energy of the system is inversely proportional to the radius of the orbit."
- **Analysis**: The total energy \( E \) of the electron in a hydrogen atom is given by \( E \propto -\frac{1}{r} \). This indicates that the total energy is indeed inversely proportional to the radius of the orbit.
- **Conclusion**: This statement is **correct**.

4. **Statement 4**: "The magnetic moment is proportional to the square of the radius of the orbit."
- **Analysis**: The magnetic moment \( \mu \) is related to the angular momentum and is given by \( \mu \propto r^2 \). This means that the magnetic moment is indeed proportional to the square of the radius of the orbit.
- **Conclusion**: This statement is **correct**.

### Final Conclusion:
The only wrong statement regarding the hydrogen atom is **Statement 1**.