If first orbit energy of `He^(+)` is -54.4 eV, then the second orbit energy will be

Options

A. `-54.4 eV`
B. `-13.6 eV`
C. `-27.2 eV`
D. `+27.2 eV`

Explanation

To find the energy of the second orbit for the ion \( He^{+} \), we can use the formula for the energy levels of hydrogen-like atoms:

\[ E_n = \frac{E_0}{n^2} \]

where:
- \( E_n \) is the energy of the nth orbit,
- \( E_0 \) is the energy of the first orbit (for hydrogen-like atoms, \( E_0 = -13.6 \, \text{eV} \) for hydrogen),
- \( n \) is the principal quantum number (1 for the first orbit, 2 for the second orbit, etc.).

### Step 1: Identify the energy of the first orbit
We know that the energy of the first orbit for \( He^{+} \) is given as \( -54.4 \, \text{eV} \).

### Step 2: Use the relationship between \( E_0 \) and the atomic number \( Z \)
For hydrogen-like ions, the energy of the first orbit can be expressed as:

\[ E_0 = -13.6 \times Z^2 \, \text{eV} \]

For \( He^{+} \), the atomic number \( Z = 2 \).

Calculating \( E_0 \):

\[ E_0 = -13.6 \times 2^2 = -13.6 \times 4 = -54.4 \, \text{eV} \]

This confirms that the given first orbit energy is correct.

### Step 3: Calculate the energy of the second orbit
Now, we need to find the energy of the second orbit (\( n = 2 \)):

\[ E_2 = \frac{E_0}{2^2} = \frac{-54.4 \, \text{eV}}{4} = -13.6 \, \text{eV} \]

### Final Answer
Thus, the energy of the second orbit for \( He^{+} \) is:

\[ \boxed{-13.6 \, \text{eV}} \]

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