We’re being asked to calculate how many photons of the lowest possible frequency are required to ionize a sample of carbon. The first ionization energy of carbon is 1.81 aJ.

*Ionization energy (IE) **is the energy required to remove an electron from **a gaseous atom **or ion. Let’s calculate the **ionization** energy in J.*

**1 aJ = 10 ^{-18} J**

$\mathit{I}\mathit{E}\mathbf{}\mathbf{=}\mathbf{}\mathbf{1}\mathbf{.}\mathbf{81}\mathbf{}\overline{)\mathbf{a}\mathbf{J}}\mathbf{}\mathbf{\times}\mathbf{}\frac{{\mathbf{10}}^{\mathbf{-}\mathbf{18}}\mathbf{}\mathbf{J}}{\mathbf{1}\mathbf{}\overline{)\mathbf{a}\mathbf{J}}}$

*IE = 1.81x10 ^{-18} J/atom*

The *ionization efficiency is 22.35%*. Calculate the energy for 22.35% ionization efficiency:

**% ionization efficiency = 22.35 %**

**Total energy = 1.81x10 ^{-18} J/atom**

The first ionization energy of carbon is 1.81 aJ. Assuming an ionization efficiency of 22.35%, how many photons of the lowest possible frequency are required to ionize a sample of carbon that contains 5.32 x 10^{18} atoms?

a) 2.38 x 10^{19} photons

b) 4.20 x 10^{-20} photons

c) 2.73 x 10^{15} photons

d) 9.11 x 10^{6} photons

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