An electron is moving in `3^(rd)` orbit of `Li^(+2)` and its separation energy is y.The separation energy of an electron moving in `2^(nd)` orbit of `He^(+)` is

Options

A. `(4y)/( 9)`
B. `(y)/(9)`
C. `-(y)/(9)`
D. `y`

Answer

To solve the problem, we need to determine the separation energy of an electron moving in the second orbit of the helium ion \( \text{He}^+ \), given that the separation energy of an electron in the third orbit of lithium ion \( \text{Li}^{2+} \) is \( y \).

### Step-by-Step Solution:

1. **Understand Separation Energy**:
The separation energy is the energy required to remove an electron from an atom or ion. It can be calculated using the formula for the energy of an electron in a given orbit.

2. **Energy Formula**:
The energy of an electron in an orbit is given by the formula:
\[ E_n = -\frac{13.6 \, \text{eV} \cdot Z^2}{n^2} \]
where \( Z \) is the atomic number and \( n \) is the principal quantum number (orbit number).

3. **Calculate Separation Energy for \( \text{Li}^{2+} \)**:
- For lithium (\( Z = 3 \)) in the third orbit (\( n = 3 \)):
\[ E_3 = -\frac{13.6 \cdot 3^2}{3^2} = -\frac{13.6 \cdot 9}{9} = -13.6 \, \text{eV} \]
- The energy at infinity \( E_\infty \) is \( 0 \, \text{eV} \).
- Therefore, the separation energy \( y \) is:
\[ y = E_\infty - E_3 = 0 - (-13.6) = 13.6 \, \text{eV} \]

4. **Calculate Separation Energy for \( \text{He}^+ \)**:
- For helium (\( Z = 2 \)) in the second orbit (\( n = 2 \)):
\[ E_2 = -\frac{13.6 \cdot 2^2}{2^2} = -\frac{13.6 \cdot 4}{4} = -13.6 \, \text{eV} \]
- Again, the energy at infinity \( E_\infty \) is \( 0 \, \text{eV} \).
- Therefore, the separation energy for helium is:
\[ \text{Separation Energy} = E_\infty - E_2 = 0 - (-13.6) = 13.6 \, \text{eV} \]

5. **Relate to \( y \)**:
Since we found that the separation energy of the electron in the second orbit of \( \text{He}^+ \) is also \( 13.6 \, \text{eV} \), and we previously established that \( y = 13.6 \, \text{eV} \), we conclude:
\[ \text{Separation Energy for } \text{He}^+ = y \]

### Final Answer:
The separation energy of an electron moving in the second orbit of \( \text{He}^+ \) is \( y \).