# Ionization energy is the energy needed to eject an electron from an atom. Compute the ionization energy of a hydrogen atom in its fourth excited state (n = 5). The ionization energy can be calculated by determining the difference between the energy of an electron in its initial state and the final state. This change in energy can be calculated by using the following equation:

Ionization energy = `E_oo - E_5`

` `

= `-R_H (1/n_f^2 - 1/n_i^2)`

where, `R_H` has a constant value of `2.179 xx 10^-18` J. Also, the energy at infinity will be zero. Substituting all the values, we get:

ionization energy =   2.179 x 10^-18 x (0 - 1/5^2)

= - 2.179 x 10^-18 x (-1/25) = 8.716 x 10^-20 J

We can convert this to the units of kJ/mol by first multiplying energy change by Avogadro's number:

Ionization energy = 8.716 x 10^-20 J/atom x 6.023 x 10^23 atoms/mole

We then multiply that number by (1 J / 1,000 kJ) to get the final answer.

= 52.49 kJ/mol (the positive sign indicates that the energy is absorbed).

Hope this helps.

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