The energy required by electrons, present in the first Bohr orbit of hydrogen atom to be excited to second Bohr orbit is _ _ _ _ J mol ⁻¹ . Given: R_ H =2.18 10⁻¹¹ ergs .

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 = E₂ - E₁ = 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