JEE Main Chemistry Question (2026) — Solution

Step-by-step solution

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