Question

O₂ molecules can dissociate to form O atoms by absorbing electromagnetic radiation. If it takes 498 kJ to dissociate one mole of O₂ molecules to form two moles of O atoms, what is the frequency of the light that would have just enough energy to decompose a single O₂ molecule into O atoms?

Answer 1

1 mole of O₂ = 6.023X10²³ molecules of O₂

Energy required to dissociate 1 mole of O₂ molecules = 498 kJ

Energy required to dissociate 1 molecule of O₂ = 498/6.023X10²³ kJ

Now apply Planck's law, which states that the energy of a quantum of radiation is directly proportional to the frequency of the radiation

E = h*f

where h is Planck's constant(6.63X10^-34 J-s) and f is the frequency.

498/6.023X10²³ = 6.63X10^-34 *f

f =  498/(6.023X10²³ )( 6.63X10^-34 )

f = 498/39.93X10^-11

f = 1.247X10¹² sec^-1

The frequency of the light that would have just enough energy to decompose a single O2 molecule into O atoms is 1.247X10¹² sec^-1