Which of the following statements (regarding an atom of H ) are correct?

Options

A. Kinetic energy of the electron is maximum in the first orbit
B. Potential energy of the electron is maximum in the first orbit
C. Radius of the second orbit is four times the redius of the first orbit
D. Various energy levels are equally spaced

Answer

To determine which statements regarding an atom of hydrogen are correct, we will analyze each statement step by step.

### Step-by-Step Solution:

1. **Statement A: Kinetic energy of the electron is maximum in the first orbit.**
- The formula for kinetic energy (KE) of an electron in an orbit is given by:
\[ KE = \frac{2 \pi^2 m e^4}{n^2 h^2} \]
- Here, \( n \) is the principal quantum number (orbital number). From the equation, we can see that kinetic energy is inversely proportional to \( n^2 \).
- As \( n \) increases, \( KE \) decreases. Therefore, the kinetic energy is maximum when \( n \) is minimum (i.e., in the first orbit where \( n = 1 \)).
- **Conclusion:** Statement A is correct.

2. **Statement B: Potential energy of the electron is maximum in the first orbit.**
- The formula for potential energy (PE) is given by:
\[ PE = -\frac{4 \pi^2 k^2 m e^4}{n^2 h^2} \]
- Potential energy is directly proportional to \( -\frac{1}{n^2} \), which means it becomes less negative (or increases) as \( n \) increases.
- Thus, the potential energy is minimum (most negative) in the first orbit and increases (becomes less negative) as \( n \) increases.
- **Conclusion:** Statement B is incorrect.

3. **Statement C: Radius of the second orbit is 4 times the radius of the first orbit.**
- The radius of an orbit is given by:
\[ r_n = k \frac{n^2}{Z} \]
- For the first orbit (\( n = 1 \)):
\[ r_1 = k \frac{1^2}{Z} = \frac{k}{Z} \]
- For the second orbit (\( n = 2 \)):
\[ r_2 = k \frac{2^2}{Z} = \frac{4k}{Z} \]
- This shows that \( r_2 = 4 \times r_1 \).
- **Conclusion:** Statement C is correct.

4. **Statement D: Various energy levels are equally spaced.**
- The energy levels of an electron in a hydrogen atom are given by:
\[ E_n = -\frac{13.6 \text{ eV}}{n^2} \]
- As \( n \) increases, the difference between successive energy levels decreases, meaning they are not equally spaced.
- **Conclusion:** Statement D is incorrect.

### Final Conclusion:
- The correct statements regarding an atom of hydrogen are:
- Statement A: Correct
- Statement B: Incorrect
- Statement C: Correct
- Statement D: Incorrect

Thus, the correct answers are **A and C**.