The energy of an electron in the first Bohr orbit of H atom is `-13.6 eV`. The possible energy values (s) of the excited state (s) for electron in bohr orbits of hydrogen is (are)

Options

A. `-3.4eV`
B. `-4.2eV`
C. `-6.8eV`
D. `+6.8eV`

Explanation

To find the possible energy values of the excited states for an electron in Bohr orbits of a hydrogen atom, we can follow these steps:

### Step 1: Understand the Energy Formula
The energy of an electron in the nth Bohr orbit of a hydrogen atom is given by the formula:
\[ E_n = -\frac{13.6 \, Z^2}{n^2} \, \text{eV} \]
where \( Z \) is the atomic number (for hydrogen, \( Z = 1 \)) and \( n \) is the principal quantum number (n = 1, 2, 3, ...).

### Step 2: Calculate the Energy for the First Orbit
For the first Bohr orbit (n = 1):
\[ E_1 = -\frac{13.6 \times 1^2}{1^2} = -13.6 \, \text{eV} \]

### Step 3: Calculate the Energy for the Second Orbit
For the second Bohr orbit (n = 2):
\[ E_2 = -\frac{13.6 \times 1^2}{2^2} = -\frac{13.6}{4} = -3.4 \, \text{eV} \]

### Step 4: Calculate the Energy for Higher Orbits
For the third Bohr orbit (n = 3):
\[ E_3 = -\frac{13.6 \times 1^2}{3^2} = -\frac{13.6}{9} \approx -1.51 \, \text{eV} \]

For the fourth Bohr orbit (n = 4):
\[ E_4 = -\frac{13.6 \times 1^2}{4^2} = -\frac{13.6}{16} = -0.85 \, \text{eV} \]

### Step 5: Generalize for Higher Excited States
The energy values for higher excited states (n = 5, 6, ...) will continue to be less negative (closer to zero) as n increases. Thus, the energies will be:
- \( E_5 \approx -0.54 \, \text{eV} \)
- \( E_6 \approx -0.38 \, \text{eV} \)
- and so on...

### Conclusion
The possible energy values of the excited states for the electron in the Bohr orbits of hydrogen are:
- \( E_2 = -3.4 \, \text{eV} \)
- \( E_3 \approx -1.51 \, \text{eV} \)
- \( E_4 \approx -0.85 \, \text{eV} \)
- Higher excited states will have energies that are less negative.

### Final Answer
The possible energy values of the excited states for the electron in Bohr orbits of hydrogen include:
- \( -3.4 \, \text{eV} \) (for n = 2)
- \( -1.51 \, \text{eV} \) (for n = 3)
- \( -0.85 \, \text{eV} \) (for n = 4)
- and so on...