An electron transits from n=3 to ground state in hydrogen atom. If K, P and T are kinetic energy, potential energy and total energy of the electron respectively, which of the following statements regarding the energy of electron is/are correct?

Options

A. Only K increases
B. Only T increases
C. Both P and T decrease
D. Both P and T increase

Explanation

To solve the problem regarding the energy of an electron transitioning from n=3 to the ground state (n=1) in a hydrogen atom, we will analyze the kinetic energy (K), potential energy (P), and total energy (T) of the electron.

### Step-by-Step Solution:

1. **Understanding Energy Levels**:
The energy levels of an electron in a hydrogen atom are given by the formula:
\[ E_n = -\frac{13.6 \, \text{eV}}{n^2} \]
where \(E_n\) is the energy at level \(n\).

2. **Calculating Total Energy**:
For n=3:
\[ E_3 = -\frac{13.6 \, \text{eV}}{3^2} = -\frac{13.6 \, \text{eV}}{9} \approx -1.51 \, \text{eV} \]
For n=1 (ground state):
\[ E_1 = -\frac{13.6 \, \text{eV}}{1^2} = -13.6 \, \text{eV} \]

3. **Change in Total Energy**:
The transition from n=3 to n=1 results in a change in total energy:
\[ \Delta E = E_1 - E_3 = -13.6 \, \text{eV} - (-1.51 \, \text{eV}) = -12.09 \, \text{eV} \]
This indicates that the total energy decreases as the electron moves to a lower energy level.

4. **Kinetic and Potential Energy Relationships**:
The total energy (T), kinetic energy (K), and potential energy (P) are related as follows:
\[ T = K + P \]
For a hydrogen atom, the potential energy is given by:
\[ P = 2T \]
Thus, we can express kinetic energy as:
\[ K = -\frac{T}{2} \]

5. **Analyzing Changes in K, P, and T**:
- Since total energy (T) decreases, kinetic energy (K) will also decrease because \(K = -\frac{T}{2}\).
- Potential energy (P) is related to total energy as \(P = 2T\), so if T decreases, P will also decrease.

6. **Conclusion**:
- Total energy (T) decreases.
- Kinetic energy (K) decreases.
- Potential energy (P) decreases.

### Summary of Statements:
- T decreases.
- K decreases.
- P decreases.

### Correct Statements:
1. K decreases.
2. P decreases.
3. T decreases.