Determine the total energy required to completely remove the electron from one mole of Li²⁺ ions that are initially present in their first excited state. (Given: Ionization energy of H atom in the ground state = 2.18 10⁻¹⁸ J atom ⁻¹ ; Avogadro's constant N_A = 6.0 10²³ mol ⁻¹ )

Step-by-step solution

For a hydrogen-like species, the energy required to remove an electron from the n^ th state to infinity is given by: E = IE_ H Z^2 n^2 For the Li²⁺ ion, the atomic number Z = 3 . The first excited state corresponds to the principal quantum number n = 2 . Energy required for a single Li²⁺ ion: E_ ion = 2.18 10⁻¹⁸ 3^2 2^2 E_ ion = 2.18 10⁻¹⁸ 9 4 E_ ion = 4.905 10⁻¹⁸ J To find the total energy for one mole of ions, multiply by Avogadro's constant: E_ total = E_ ion N_A E_ total = 4.905 10⁻¹⁸ 6.0 10²³ E_ total = 29.43