The ground state energy in J, of hydrogen atom is –X. The minimum energy in J, required to promote an electron from n=1 to n=2 in He⁺ is

Energy of hydrogen atom in any orbit is calculated as:

${\mathrm{E}}_{\mathrm{n}}=-\frac{{\mathrm{XZ}}^2}{{\mathrm{n}}^2}$

For He⁺, the value of Z is 2.

$$\begin{gathered} {\mathrm{E}}_1=\frac{-\mathrm{X}{2}^2}{1^2}=-4\mathrm{X} \mathrm{J} \\ {\mathrm{E}}_2=\frac{-\mathrm{X}{2}^2}{2^2}=-\mathrm{X} \mathrm{J} \end{gathered}$$

Difference between energy between n=1 and n=2 is:

$$\begin{gathered} ∆\mathrm{E}={\mathrm{E}}_2-{\mathrm{E}}_1 \\ ∆\mathrm{E}=-\mathrm{X} \mathrm{J}-\left(-4\mathrm{X} \mathrm{J}\right)=3\mathrm{XJ} \end{gathered}$$