Ionization energy - 2 | Quantum Theory and Atomic Structure

First ionization energy: H(g) → H⁺(g) + e^-

E_{ion-1electron} = E_f – E_i

The atom is initially in the ground state (n = 1).

At the end, the atom is ionized ⇒ the electron is no longer bound to the atom (n = ∞).

E_∞ > E₁ ⇒ E_{ion-1electron} = E_∞ – E₁ = (2.1799 x 10^-18) x ( – 0) = 2.180 x 10^-18 J.

The ionization energy of hydrogen represents the energy required to remove 1 mole of electrons from 1 mole of hydrogen atoms in the gaseous state.

E_ionization = n x E_{ion-1electron}   where n = number of electrons in 1 mole = N_A

E_ionization = 6.022 x 10²³ x 2.180 x 10^-18 = 1.31 x 10⁶ J.