If `E_(p) and E_(x)` represent potential energy and kinetic energy.respectively, of an orbital electron, then, according to Bohr.s theory :

Options

A. `E_(k)=-E_(p)//2`
B. `E_(k)=-E_(p)`
C. `E_(k)=-2E_(P)`
D. `E_(k)2E_(P)`

Answer

To solve the problem regarding the relationship between potential energy (E_p) and kinetic energy (E_k) of an orbital electron according to Bohr's theory, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Definitions**:
- The potential energy (E_p) of an electron in orbit is given by the formula:
\[ E_p = -\frac{Z e^2}{r} \]
- The kinetic energy (E_k) of the electron is given by the formula:
\[ E_k = \frac{Z e^2}{2r} \]
Here, \(Z\) is the atomic number, \(e\) is the charge of the electron, and \(r\) is the radius of the orbit.

2. **Finding the Ratio of Potential Energy to Kinetic Energy**:
- To find the relationship between E_p and E_k, we can take the ratio of E_p to E_k:
\[ \frac{E_p}{E_k} = \frac{-\frac{Z e^2}{r}}{\frac{Z e^2}{2r}} \]

3. **Simplifying the Ratio**:
- Simplifying the above expression:
\[ \frac{E_p}{E_k} = \frac{-\frac{Z e^2}{r}}{\frac{Z e^2}{2r}} = \frac{-2}{1} = -2 \]

4. **Expressing Kinetic Energy in Terms of Potential Energy**:
- From the ratio, we can express kinetic energy in terms of potential energy:
\[ E_k = -\frac{E_p}{2} \]

5. **Conclusion**:
- Therefore, the relationship between the potential energy and kinetic energy of an orbital electron according to Bohr's theory is:
\[ E_k = -\frac{E_p}{2} \]

### Final Answer:
The correct relationship is:
\[ E_k = -\frac{E_p}{2} \]