An electron in a hydrogen atom makes a transition such that its kinetic energy increases, then

Options

A. The electron may have excited form n=2 to n=3
B. Potential energy of the electron increases
C. Potential energy of the electron decreases
D. Total energy of the electron increases

Answer

To solve the problem, we need to analyze the transition of an electron in a hydrogen atom and how it affects its kinetic and potential energy.

### Step-by-Step Solution:

1. **Understanding Kinetic Energy in Hydrogen Atom:**
The kinetic energy (KE) of an electron in a hydrogen atom is given by the formula:
\[ KE = -\frac{1}{2} \times \text{Total Energy} \]
The total energy (E) of the electron in the nth orbit is given by:
\[ E = -\frac{13.6 \, \text{eV}}{n^2} \]
Therefore, the kinetic energy can be expressed as:
\[ KE = -\left(-\frac{13.6 \, \text{eV}}{n^2}\right) \times \frac{1}{2} = \frac{13.6 \, \text{eV}}{2n^2} \]

2. **Effect of Transition on Kinetic Energy:**
If the kinetic energy of the electron increases, it implies that the value of \( KE \) is increasing. Since \( KE \) is inversely proportional to \( n^2 \), an increase in kinetic energy means that \( n \) must decrease (i.e., the electron is moving to a lower energy level).

3. **Evaluating the Options:**
- **Option A:** Transition from \( n=2 \) to \( n=3 \) - This is incorrect because \( n \) is increasing, which contradicts our finding that \( n \) must decrease for kinetic energy to increase.
- **Option B:** Potential energy of the electron increases - This is incorrect. As \( n \) decreases, the potential energy, which is given by:
\[ PE = 2 \times E = -\frac{27.2 \, \text{eV}}{n^2} \]
also decreases (becomes more negative).
- **Option C:** Potential energy of the electron decreases - This is correct. Since \( n \) decreases, the potential energy becomes more negative, indicating a decrease in potential energy.

4. **Conclusion:**
The correct answer is that the potential energy of the electron decreases when its kinetic energy increases.