Potential energy `(PE_(n))` and kinetic energy `(KE_(n))` of electron in nth orbit are related as

Options

A. `PE_(n)=KE_(n)`
B. `PE_(n)=-2KE_(n)`
C. `PE_(n)=2KE_(n)`
D. `PE_(n)=KE_(n)`

Answer

To solve the question regarding the relationship between the potential energy (PE) and kinetic energy (KE) of an electron in the nth orbit, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Definitions**:
- The potential energy (PE) of an electron in an orbit is the energy due to its position in the electric field created by the nucleus.
- The kinetic energy (KE) of an electron is the energy due to its motion.

2. **Recall the Relationships**:
- In atomic physics, particularly in the Bohr model of the hydrogen atom, the potential energy (PE) and kinetic energy (KE) of an electron in an orbit are related to the total energy (E) of the system.
- The total energy (E) of the electron in the nth orbit is given by:
\[ E_n = KE_n + PE_n \]

3. **Use Known Relationships**:
- It is known that:
\[ PE_n = 2E_n \quad \text{(1)} \]
\[ KE_n = -E_n \quad \text{(2)} \]

4. **Substituting Total Energy**:
- From equation (2), we can express the total energy in terms of kinetic energy:
\[ E_n = -KE_n \]
- Now substituting this into equation (1):
\[ PE_n = 2(-KE_n) = -2KE_n \]

5. **Final Relationship**:
- Therefore, we arrive at the relationship:
\[ PE_n = -2KE_n \]

6. **Select the Correct Option**:
- From the options given, we see that the correct relationship is:
\[ PE_n = -2KE_n \]
- Hence, the correct answer is **Option 2**.