Exercise 10 | Early Quantum Theory
Determine the first ionization energy of a hydrogen atom in the ground state.
First ionization energy: H(g) → H+(g) + e-
Eion-1electron = Ef – Ei
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 ⇒ Eion-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.
Eionization = n x Eion-1electron where n = number of electrons in 1 mole = NA
Eionization = 6.022 x 1023 x 2.180 x 10-18 = 1.31 x 106 J.