When a hydrogen atom is raised the ground state to third state

Options

A. Both kinetic energy and potential energy increase
B. Both Kinetic energy and potential energy decreases
C. Potential energy increases and kinetic energy decreases
D. Potential energy decreases and kinetic energy increases

Answer

To solve the problem of how the kinetic energy and potential energy of a hydrogen atom change when it is raised from the ground state (n=1) to the third state (n=3), we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Ground State and Third State**:
- The ground state of a hydrogen atom corresponds to n = 1.
- The third state corresponds to n = 3.

2. **Kinetic Energy Formula**:
- The kinetic energy (KE) of an electron in a hydrogen atom is given by the formula:
\[ KE = \frac{13.6 \, \text{eV}}{n^2} \]
- For n = 1 (ground state):
\[ KE_1 = \frac{13.6 \, \text{eV}}{1^2} = 13.6 \, \text{eV} \]
- For n = 3 (third state):
\[ KE_3 = \frac{13.6 \, \text{eV}}{3^2} = \frac{13.6 \, \text{eV}}{9} \approx 1.51 \, \text{eV} \]

3. **Potential Energy Formula**:
- The potential energy (PE) of the electron is related to the kinetic energy by:
\[ PE = -2 \times KE \]
- For n = 1:
\[ PE_1 = -2 \times 13.6 \, \text{eV} = -27.2 \, \text{eV} \]
- For n = 3:
\[ PE_3 = -2 \times 1.51 \, \text{eV} \approx -3.02 \, \text{eV} \]

4. **Analyze the Changes in Energy**:
- **Kinetic Energy**:
- From 13.6 eV (n=1) to approximately 1.51 eV (n=3), the kinetic energy decreases.
- **Potential Energy**:
- From -27.2 eV (n=1) to approximately -3.02 eV (n=3), the potential energy increases (the magnitude decreases, but since it's negative, it approaches zero).

5. **Conclusion**:
- When the hydrogen atom is raised from the ground state to the third state:
- The kinetic energy decreases.
- The potential energy increases (in magnitude, it decreases but approaches zero).

### Final Answer:
- **Kinetic Energy**: Decreases
- **Potential Energy**: Increases