Question

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

Answer 1

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. 

Answer 2

Answer;

Wavelength= 1197.47 nm

Explanation and solution;

1.0x10^2 kJ/mole x (1 mole / 6.022x10^23 photons) x (1000 J / 1 kJ)

= 1.66 x10^-19 J/photon

Energy of a wave = ħc / λ  

where;

E = energy of the wave = = 1.66 x10^-19 J/photon

ħ = plancks constant = 6.626x10^-34 J s  

c = speed of light = 3.00x10^8 m/s  

λ = wavelength

λ = ħc / E

   = (6.626x10^-34 J s) x (3.00x10^8 m/s) / (1.66 x10^-19 J)  

λ = 1.197 x10^-6 m x (1x10^9 nm / m)  

   = 1197.47 nm