Question

# O2 molecules can dissociate to form O atoms by absorbing electromagnetic radiation. If it takes 498...

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?

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

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