Wavelength when given energy?

Question

I'm being asked to find the wavelength in nm of three possible electronic transitions of Lithium. The three energies given are 178 kJ/mol, 370 kJ/mol, and 375 kJ/mol,

I can't figure out how to get the wavelength from this. I tried using L=hc/E but I end up getting something crazy

Answer 1

You have the right formula, but it's probably unit conversions. The transitions are given in kJ/mol, so you have to convert that to J's. That will tell you the energy of a whole mole of photons, you need to divide by Avagadro's # to get the energy of a single photon, then use THAT energy in your formula. It will give you an answer in units of m.

By the way kJ/mole is a wierd way to specific photon energy, make sure the units are right on that

Answer 2

L=hc/E
h=6.626e-34 Js
c=2.99e8 m/2

So, for instance, 150 kJ/mol = 150 (kJ/mol)(1 mol/6.022e23 atom) = ~25e-23 kJ = 25e-20 J
L=hc/E would then be 0.088e-6 m. Most likely you just need to check your units.

Answer 3

first convert kJ/mole in J/molecule.
For this you must divide the energy by Avogadro's number
I give you example for 178kJ/mole= 178*10^3J/mole
than divide by avogadro's number 6.02210^23
you obtain 3*10^-19J/molecule

and use your formula L = hc/E= 6.62*10^-34*3*10^8/3*10^-19
you find 6.62 *10^-7m

for 370kJ/mole you find 3.22 10^-7m
and 3.18*10^-7m for 375kJ/mole