Problem: 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 1018 atoms?a) 2.38 x 1019 photonsb) 4.20 x 10-20 photonsc) 2.73 x 1015 photonsd) 9.11 x 106 photons 

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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

IE = 1.81 aJ × 10-18 J1 aJ

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

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Problem Details

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 1018 atoms?

a) 2.38 x 1019 photons

b) 4.20 x 10-20 photons

c) 2.73 x 1015 photons

d) 9.11 x 106 photons 

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