Electronic StructureMedium

Ionization energy

The ionization energy of hydrogen is 13.6 eV. Calculate the energy needed to ionize a hydrogen atom from level n=2.
E_n = -13.6/n² eV.

Given data

I.E. = 13.6 eVE_n = -13.6/n² eV

Steps

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Calculate the energy of level n=2.
Write your working — the numerical result must appear in the text eV
Calculate the energy needed to take the electron from n=2 to n=∞ (E=0).

Full worked solution

Calculate the energy of level n=2.
$E_2 = -\frac{13.6}{4}$
$E_2 = -13.6/2^2 = -13.6/4 = \mathbf{-3.40\,eV}$ . The energy of level n=2 is obtained by substituting n=2 into the Bohr formula.
Calculate the energy needed to take the electron from n=2 to n=∞ (E=0).
$\Delta E = 0 - E_2$
$\Delta E = 0 - E_2 = 0 - (-3.40) = \mathbf{3.40\,eV}$ . The energy required to ionize hydrogen from level n=2 is 3.40 eV.

Result:Need 3.40 eV to ionize H from n=2.

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