If an electron's energy in the ground state of a hydrogen atom is -x eV , then energy in the second

Question

If an electron's energy in the ground state of a hydrogen atom is -x eV , then energy in the second excited state of $\mathrm{He}^{+}$is

Professor PC Thomas Classes · Answer

$E \propto \frac{Z^2}{n^2}$. Ground state H ($Z=1, n=1$) is $-x$.\ Second excited state He$^+$ ($Z=2, n=3$) is $-x(2^2/3^2) = -4x/9$.