How do you calculate the ionization energy of a hydrogen atom in its ground state?

By using the Rydberg expression:

The wavelength λ of the emission line in the hydrogen spectrum is given by:


R is the Rydberg Constant and has the value 1.097×107m−1

n1 is the principle quantum number of the lower energy level

n2 is the principle quantum number of the higher energy level.

The energy levels in hydrogen converge and coalesce:

The electron is in the n1=1 ground state we need to consider series 1. These transitions occur in the u.v part of the spectrum and is known as The Lyman Series. The 1/n22 decreases.

The Rydberg expression then written as


Since n1=1 this becomes:









This is the energy needed to remove 1 electron from 1 hydrogen atom. To find the energy required to ionize 1 mole of H atoms we multiply by the Avogadro Constant:



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