In Bohr's model of hydrogen atom, let `PE` represents potential energy and `TE` the total energy. In going to a higher level

Options

A. PE increase and TE decrease
B. PE decrease and TE increase
C. PE increase and TE increase
D. PE decrease and TE decrease

Explanation

To solve the question regarding the changes in potential energy (PE) and total energy (TE) in Bohr's model of the hydrogen atom when moving to a higher energy level, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Potential Energy (PE)**:
- In Bohr's model, the potential energy (PE) of an electron in a hydrogen atom is given by the formula:
\[ PE = -\frac{kZe^2}{r} \]
where \( k \) is a constant, \( Z \) is the atomic number (which is 1 for hydrogen), \( e \) is the charge of the electron, and \( r \) is the radius of the orbit.

2. **Relationship between Radius and Principal Quantum Number (n)**:
- The radius \( r \) of the electron's orbit is directly proportional to the square of the principal quantum number \( n \):
\[ r \propto n^2 \]
- As \( n \) increases (moving to a higher energy level), the radius \( r \) also increases.

3. **Effect on Potential Energy**:
- Since \( r \) increases when \( n \) increases, the numerical value of the potential energy becomes less negative (i.e., it increases).
- For example, if \( n \) goes from 1 to 2, the potential energy changes from a more negative value to a less negative value:
\[ PE \text{ increases (less negative)} \]

4. **Understanding Total Energy (TE)**:
- The total energy (TE) of the electron is given by:
\[ TE = PE + KE \]
where KE is the kinetic energy. In Bohr's model, the total energy can also be expressed as:
\[ TE = -\frac{m k^2 Z^2 e^4}{2 n^2} \]
- This formula shows that total energy is also negative and is inversely proportional to \( n^2 \).

5. **Effect on Total Energy**:
- As \( n \) increases, the absolute value of total energy decreases (becomes less negative). Therefore, the total energy increases:
\[ TE \text{ increases (less negative)} \]

6. **Conclusion**:
- From the analysis, we conclude that when moving to a higher energy level:
- Potential energy increases (becomes less negative).
- Total energy increases (becomes less negative).
- Therefore, the correct option is:
- **Option 3**: Potential energy increases, total energy increases.