JEE Main 2026 — Structure of Atom Question with Solution

The energy of an electron in the $n^{th}$ Bohr orbit of a hydrogen atom is given by $E_n=-R_H\left(\frac{1}{n^2}\right)$.
The energy required for excitation from $n=1$ to $n=2$ for a single atom is $\Delta E=E_2-E_1=R_H\left(\frac{1}{1^2}-\frac{1}{2^2}\right)=R_H\left(1-\frac{1}{4}\right)=\frac{3}{4}{R}_H$.
Given $R_H=2.18\times 10^{-11}$ ergs.
Converting ergs to Joules: $1\text{ erg}=10^{-7}\text{ J}$.
So, $R_H=2.18\times 10^{-11}\times 10^{-7}=2.18\times 10^{-18}\text{ J}$.
The energy required per atom is $\Delta E=\frac{3}{4}\times 2.18\times 10^{-18}=1.635\times 10^{-18}\text{ J}$.
To find the energy required per mole of electrons, multiply by Avogadro's number $N_A\approx 6.022\times 10^{23}{\text{ mol}}^{-1}$.
Energy per mole $=1.635\times 10^{-18}\times 6.022\times 10^{23}{\text{ J mol}}^{-1}$.
Energy per mole $\approx 9.846\times 10^5{\text{ J mol}}^{-1}$.
Comparing with the given options, $9.835\times 10^5$ is the closest value.