Question

What is the wavelength (in nm) of radiation that has an energy content of 9.39 x 10^3 kJ/mol? In which region of the electromagnetic spectrum is this radiation found?

Answer 1

Energy content = 9.39 x 10³ kJ/mol

So,

9.39 x 10³ kJ/mole x (1 mole / 6.022 x 10²³ photons) x (1000 J / 1 kJ)

= 1.56 x 10^-17 J/photon

We know that;

E = hc /

where;

E = energy of a photon = 1.56 x 10^-17 J
h = plancks constant = 6.626 x 10^-34 J s
c = speed of light = 3.00 x 10⁸ m/s
= wavelength = ?

= hc / E

= [ (6.626 x 10^-34 J s) x (3.00 x 10⁸ m/s) ] / (1.56 x 10^-17 J)

= 12.74 x 10^-9 m

= 12.74 nm

This falls into the range of the Ultraviolet region (10 nm to 400 nm) of the electromagnetic spectrum.