The ratio of the total energy of the $2^{\text {nd }}$ orbit electron for the hydrogen atom $1 \mathrm{H}^1$ to that of helium ion $\left(\mathrm{He}^{+}\right) 2 \mathrm{He}^4$ is

Total energy of an electron in a hydrogen-like atom: $E_n = -13.6 \frac{Z^2}{n^2}$ eV

For hydrogen ($Z = 1$ in the $n = 2$ orbit): $E_{H,2} = -13.6 \frac{1^2}{2^2} = -3.4$ eV

For helium ion He⁺ ($Z = 2$ in the $n = 2$ orbit): $E_{He,2} = -13.6 \frac{2^2}{2^2} = -13.6$ eV

The energy ratio is $\frac{E_{H,2}}{E_{He,2}} = \frac{-3.4}{-13.6} = \frac{1}{4}$