Energy Levels Of Hydrogen

The bound energy levels of hydrogen are given by $E_n=-\frac{13.6}{n^2}$ eV, where the negative sign signifies that the electron is trapped in the potential well of the proton. The first excited state corresponds to $n=2$, so $E_2=-\frac{13.6}{2^2}=-\frac{13.6}{4}=-3.4$ eV. The value -13.6 eV is the ground-state energy for $n=1$ and therefore does not apply to the first excited state. The value -1.51 eV corresponds to $n=3$, the second excited state, not the requested level. The value -6.8 eV incorrectly divides by 2 instead of $2^2=4$, ignoring the inverse-square dependence on $n$. This is the standard NCERT energy-level formula derived from the Bohr model. A plausibility check confirms the answer: excited states must lie higher (less negative) than the ground state, and indeed -3.4 eV is greater than -13.6 eV, which is exactly what we expect for an electron promoted away from the nucleus.