What is the wavelength (in nm) of radiation that has an energy content of 1.0x10^2 kJ/mol?

Energy = h nu, where nu is the frequency

h = 6.63 x 10^-34 J-s, Planck's constant

So nu = E/h = 1 x 10^5 J / h = 0.15 x 10^29 / s

nu lambda = c, the speed of light.

lambda = wavelength = c / nu = 3 x 10^8 / 0.15 x 10^29 = 20 x 10^-21 m.

this can possibly be a gamma ray. Gamma rays are very penetrating. It's both matter and an energy. They are electromagnetic radiation that results from a radioactive material.