The energy of an electron in the first level of H atom is `- 13.6 eV` .The possible values of the excited states for electron in `He^(o+)` is (are) :

Options

A. `-54.4 eV`
B. `-13.6 eV`
C. `-3.4 eV`
D. `-6.4 eV`

Explanation

To determine the possible values of the excited states for the electron in the He^(o+) ion, we can use the formula for the energy of an electron in a hydrogen-like atom:

\[ E_n = -\frac{13.6 \, \text{eV} \cdot Z^2}{n^2} \]

Where:
- \( E_n \) is the energy of the electron at the principal quantum number \( n \).
- \( Z \) is the atomic number of the element (for He, \( Z = 2 \)).
- \( n \) is the principal quantum number (1, 2, 3,...).

### Step 1: Calculate the energy for the first level (n=1)
For the first level (n=1):
\[ E_1 = -\frac{13.6 \cdot 2^2}{1^2} \]
\[ E_1 = -\frac{13.6 \cdot 4}{1} \]
\[ E_1 = -54.4 \, \text{eV} \]

### Step 2: Calculate the energy for the second level (n=2)
For the second level (n=2):
\[ E_2 = -\frac{13.6 \cdot 2^2}{2^2} \]
\[ E_2 = -\frac{13.6 \cdot 4}{4} \]
\[ E_2 = -13.6 \, \text{eV} \]

### Step 3: Calculate the energy for the third level (n=3)
For the third level (n=3):
\[ E_3 = -\frac{13.6 \cdot 2^2}{3^2} \]
\[ E_3 = -\frac{13.6 \cdot 4}{9} \]
\[ E_3 = -\frac{54.4}{9} \]
\[ E_3 \approx -6.04 \, \text{eV} \]

### Step 4: Calculate the energy for the fourth level (n=4)
For the fourth level (n=4):
\[ E_4 = -\frac{13.6 \cdot 2^2}{4^2} \]
\[ E_4 = -\frac{13.6 \cdot 4}{16} \]
\[ E_4 = -\frac{54.4}{16} \]
\[ E_4 = -3.4 \, \text{eV} \]

### Summary of Results
- \( E_1 = -54.4 \, \text{eV} \) (not an excited state)
- \( E_2 = -13.6 \, \text{eV} \) (not an excited state)
- \( E_3 \approx -6.04 \, \text{eV} \) (excited state)
- \( E_4 = -3.4 \, \text{eV} \) (excited state)

### Conclusion
The possible values of the excited states for the electron in He^(o+) are:
- \( E_3 \approx -6.04 \, \text{eV} \)
- \( E_4 = -3.4 \, \text{eV} \)

### Final Answer
The correct options for the excited states are:
- Option 3: \( -6.04 \, \text{eV} \)
- Option 4: \( -3.4 \, \text{eV} \)