Question

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 5.32x10^18 atoms?

Answer 1

The energy is related to frequency and wavelength as

Where

h= planck' constant = 6.63 X 10^-34 J s

Energy= 1.81 atto Joules = 1.81 X 10^-18 Joules

Frequency = 1.81 X 10^-18 Joules / 6.63 X 10^-34 J s

Frequency = 2.73 X 10^15 s^-1

Wavelength = 6.63 X 10^-34 J s X 3 X 10^8 m/s / 1.81 X 10^-18 Joules = 1.099 X 10^-7 meters = 109.9 nm

The energy required to ionize = 22.35% X 1.81 X 10^-18 Joules = 0.4045 X 10^-18 Joules

The number of photons needed = Energy X Number of atoms / available energy

                     = 1.81 X 10^-18 Joules X 5.32 × 10¹⁸  / 0.4045 X 10^-18 Joules

= 2.38X 10^19 photons