The electron in a hydrogen atom makes a transition from an excited state to the ground state. Which of the following statements is true?

Options

A. Its kinetic energy increases and its potential and total energy decreases
B. Its kinetic energy decreases, potential energy increases and its total energy remains the same
C. Its kinetic and total energy decreases and its potential energy increases
D. Its kinetic, potential and total energy decrease

Explanation

To solve the question regarding the transition of an electron in a hydrogen atom from an excited state to the ground state, we need to analyze the changes in kinetic energy, potential energy, and total energy during this transition. Here’s a step-by-step breakdown:

### Step-by-Step Solution:

1. **Understand the Transition**:
- The electron transitions from an excited state (higher energy level) to the ground state (lowest energy level). This transition involves a change in energy.

2. **Potential Energy Calculation**:
- The potential energy (PE) of the electron in a hydrogen atom is given by the formula:
\[ PE = -\frac{kZe^2}{r} \]
where \( k \) is Coulomb's constant, \( Z \) is the atomic number (1 for hydrogen), \( e \) is the charge of the electron, and \( r \) is the distance from the nucleus.

3. **Effect of Transition on Distance**:
- As the electron moves from the excited state to the ground state, the distance \( r \) decreases. Since potential energy is inversely proportional to \( r \), a decrease in \( r \) results in an increase in the magnitude of potential energy (but it remains negative).

4. **Change in Potential Energy**:
- Therefore, during the transition, the potential energy decreases (becomes more negative).

5. **Kinetic Energy Calculation**:
- The kinetic energy (KE) of the electron is related to the potential energy. In a stable orbit:
\[ KE = -\frac{1}{2} PE \]
- Since the potential energy decreases (becomes more negative), the kinetic energy must increase.

6. **Total Energy Calculation**:
- The total energy (TE) of the system is the sum of kinetic and potential energy:
\[ TE = KE + PE \]
- Since the kinetic energy increases and the potential energy decreases (becomes more negative), the total energy will also decrease.

7. **Conclusion**:
- From the analysis, we conclude:
- Kinetic energy increases.
- Potential energy decreases.
- Total energy decreases.

8. **Identify the Correct Statement**:
- Based on the changes observed, the correct statement is that kinetic energy increases, while potential energy and total energy decrease.

### Final Answer:
The true statement is: **Kinetic energy increases, potential energy decreases, and total energy decreases.**