The values of potential energy, kinetic energy and the total energy of the electron in the fourth orbit of hydrogen atom are respectively.

Options

A. `-1.7 eV, +1.7 eV,0`
B. `-1.7 eV, -1.7 eV, -3.4 eV`
C. `+1.7 eV, +1.7 eV, -3.4 eV`
D. `-1.7 eV, +0.85 eV, -0.85 eV`

Answer

To find the values of potential energy, kinetic energy, and total energy of the electron in the fourth orbit of a hydrogen atom, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Energy Relationships**:
- In a hydrogen atom, the potential energy (PE), kinetic energy (KE), and total energy (TE) are related. The potential energy is given by \( PE = -\frac{ke^2}{r} \) and the kinetic energy is given by \( KE = \frac{1}{2}mv^2 \).

2. **Using Bohr's Model**:
- According to Bohr's model, the total energy of an electron in the nth orbit is given by:
\[ E_n = -\frac{13.61 \, \text{eV}}{n^2} \]
- For the fourth orbit (\( n = 4 \)):
\[ E_4 = -\frac{13.61 \, \text{eV}}{4^2} = -\frac{13.61 \, \text{eV}}{16} = -0.85125 \, \text{eV} \approx -0.85 \, \text{eV} \]

3. **Finding Kinetic Energy**:
- The kinetic energy is related to the total energy by the equation:
\[ KE = -\frac{1}{2} E_n \]
- Therefore, substituting the total energy:
\[ KE = -\frac{1}{2} \times (-0.85 \, \text{eV}) = 0.425 \, \text{eV} \]

4. **Finding Potential Energy**:
- The potential energy is related to the kinetic energy by:
\[ PE = -2 \times KE \]
- Thus, substituting the kinetic energy:
\[ PE = -2 \times 0.425 \, \text{eV} = -0.85 \, \text{eV} \]

5. **Final Values**:
- Therefore, the values of potential energy, kinetic energy, and total energy for the electron in the fourth orbit of the hydrogen atom are:
- Potential Energy \( PE = -0.85 \, \text{eV} \)
- Kinetic Energy \( KE = 0.425 \, \text{eV} \)
- Total Energy \( TE = -0.85 \, \text{eV} \)

### Summary:
- **Potential Energy (PE)**: \(-0.85 \, \text{eV}\)
- **Kinetic Energy (KE)**: \(0.425 \, \text{eV}\)
- **Total Energy (TE)**: \(-0.85 \, \text{eV}\)