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 energies decrease.
B. Its kinetic energy decreases, potential increases and its total energy remain tha same
C. Its kinetic energy and total energies decrease, and its potential, energy increases.
D. Its kinetic potential and total energies decrease.

Explanation

To solve the problem of the transition of an electron in a hydrogen atom from an excited state to the ground state, we will analyze the changes in kinetic energy, potential energy, and total energy during this transition.

### Step-by-Step Solution:

1. **Understanding Energy Levels**:
- In a hydrogen atom, electrons occupy specific energy levels. The ground state is the lowest energy level (n=1), while excited states are higher energy levels (n=2, n=3, etc.).

**Hint**: Remember that energy levels are quantized, and transitions occur between these discrete levels.

2. **Transition from Excited State to Ground State**:
- When an electron transitions from an excited state to the ground state, it moves closer to the nucleus. This means the distance (R) between the electron and the nucleus decreases.

**Hint**: Think about how the distance from the nucleus affects potential energy.

3. **Potential Energy (PE)**:
- The potential energy of an electron in a hydrogen atom is given by the formula:
\[ PE = -\frac{kze^2}{R} \]
- As R decreases (the electron moves closer), the absolute value of PE becomes larger (less negative), indicating that potential energy is decreasing.

**Hint**: A more negative value means lower potential energy.

4. **Kinetic Energy (KE)**:
- The kinetic energy is related to the potential energy by the formula:
\[ KE = \frac{1}{2} \left| PE \right| \]
- Since potential energy is decreasing (becoming less negative), the kinetic energy will increase as R decreases.

**Hint**: Remember that kinetic energy is directly related to the absolute value of potential energy.

5. **Total Energy (E)**:
- The total energy of the system is the sum of kinetic and potential energy:
\[ E = KE + PE \]
- Since PE is decreasing (becoming less negative) and KE is increasing, we need to analyze the overall effect. The total energy, which is also negative, will decrease as the electron transitions to a lower energy state.

**Hint**: Total energy is the sum of kinetic and potential energy, and it is important to consider the signs of these energies.

6. **Conclusion**:
- From the analysis:
- Potential Energy (PE) decreases.
- Kinetic Energy (KE) increases.
- Total Energy (E) decreases.
- Therefore, the correct statement is that kinetic energy increases, while potential energy and total energy decrease.

### Final Answer:
The correct option is that kinetic energy increases, while potential energy and total energy decrease.