Question

Radiation in the ultraviolet region of the electromagnetic spectrum is quite energetic. It is this radiation that causes dyes to fade and your skin to develop a sunburn. If you are bombarded with 1.00 mol of photons with a wavelength of 345 nm, what amount of energy, in kilojoules per mole of photons, are you being subjected to? Energy = kJ/mol

Answer 1

We know for 1 mole of photons that have the wavelength $\lambda$, energy E is expressed as E = hcN/$\lambda$

where h is Planck's constant (h = 6.626 x 10–34 J s), c is the speed of light, is 2.998 x 108 m s–1, N is the Avogadro's number.

Here as provided, $\lambda$ = 345 nm = 345 x 10-9 m.

So putting this value of $\lambda$ in the above-menti$\times$oned equation, E = {(6.626 x 10–34 J s)(2.998 x 108 m s–1)(6.02214 x 1023 mol-1) / (345 x 10-9 m) = 3.46749 x 105 Jmol-1.