Calculate the energy associated with the first orbit of $He^{+}$. What is the radius of this orbit?

(N/A) The energy of an electron in the $n^{th}$ orbit is given by the formula: $E_{n} = -\frac{(2.18 \times 10^{-18} \, J) Z^{2}}{n^{2}}$.
For $He^{+}$,the atomic number $Z = 2$ and for the first orbit $n = 1$.
Substituting these values: $E_{1} = -\frac{(2.18 \times 10^{-18} \, J) (2^{2})}{1^{2}} = -8.72 \times 10^{-18} \, J$.
The radius of the $n^{th}$ orbit is given by the formula: $r_{n} = \frac{(0.0529 \, nm) n^{2}}{Z}$.
Substituting $n = 1$ and $Z = 2$: $r_{1} = \frac{(0.0529 \, nm) (1^{2})}{2} = 0.02645 \, nm$.