Wavelength and energy question?

Question

A fluorescent mineral absorbs black light from a mercury lamp. It then emits visible lights with a wavelength 520 nm. The energy not converted to light is converted to heat. If the mineral has absorbed energy with a wavelength of 320 nm, how much energy (in kJ/mol) was converted to heat?

I cant seem to visualize/get started on this problem, I imagine Ill have to find frequency to get the energy, but I dont see how ill end up with kJ/mol... Any help would be much appreciated.

Answer 1

Energy in: go from 320 nm to frequency, multiply by Planck's constant. Energy out: do the same for 520 nm. Difference is heat.

Care! units must be consistent. You want frequency in s-1, and you are presumably using

wavelength x frequency = 2.998 x10^8 m s-1

So you need to express the wavelength in m

You're not finished yet. You just found the heat per individual photon, so you need to multiply by Avogadro's number to get the answer per mol of photons.

Answer 2

First work on individual photons and individual atoms/molecules and use E=hf where f is frequency
c=f(lambda) so f=c/(lambda)
E=hc/(lambda)
=hc/320 for the lamp
The material emmits energy at a new frequency (one photon for one photon)
E=hc/520 +Et where Et is thermal energy
hc/320=hc/520+Et
Et=hc/320-hc/520
=hc(52/1664-32/1664)
=hc(5/416) this is the energy per atom/molecule
Em=Ahc(5/416) this is the energy per mol
wher h is planks constant,c is the velocity of light and A is Avagadro's number
and c=520fm for the material
320