Bohr Model Energy

For a hydrogen-like ion with a single electron, NCERT's Bohr analysis gives the energy levels as $E_n=-13.6\frac{Z^2}{n^2}$ eV, where $Z$ is the nuclear charge. The energy scales as the square of the atomic number because a larger nuclear charge binds the electron more tightly. Singly ionised helium has $Z=2$, and the ground state has $n=1$, so $E_1=-13.6\times \frac{4}{1}=-54.4$ eV. The value $-13.6$ eV is wrong because that is hydrogen's ground state with $Z=1$ and ignores the $Z^2$ factor. The value $-27.2$ eV is wrong because it scales linearly with $Z$ rather than as $Z^2$. The value $-6.8$ eV is wrong because it divides rather than multiplies by $Z^2$, loosening the binding instead of tightening it. As stated in NCERT Class 12, Chapter 12 (Atoms), hydrogen-like ions such as He+ and Li2+ follow the same Bohr formula scaled by nuclear charge, since each still has only one electron orbiting a point charge. The stronger nuclear attraction also pulls the orbits inward, shrinking the radius by a factor of $Z$, which is the geometric counterpart of the deeper energy. A magnitude check: doubling the charge quadruples the binding energy, so $-54.4$ eV being exactly four times $-13.6$ eV confirms the $Z^2$ dependence.