The energy of an electron in the first Bohr orbit of the hydrogen atom is $-13.6\text{ eV}$. What is the energy of an electron in the second Bohr orbit of the ${\text{He}}^{+}$ ion?

Solution

1. The energy of an electron in a hydrogen-like species is given by $E_n=-13.6\times \frac{Z^2}{n^2}\text{ eV}$.
2. For ${\text{He}}^{+}$, the atomic number $Z=2$ and the orbit $n=2$.
3. Substituting the values, $E_2=-13.6\times \frac{2^2}{2^2}\text{ eV}$.
4. Calculating the expression gives $E_2=-13.6\text{ eV}$.
5. Hence the answer is (A).