Chemistry--How do I find number of photons given wavelength, mass, and temperature change?

Question

Microwaves are used to heat food in microwave ovens. The microwave radiation is absorbed by moisture in the food. This heats the water, and as water becomes hot, so does the food. How many photons having a wavelength of 3.00 mm would have to be absorbed by 1.00 g of water to raise its temperature by 1.00C? It takes 4.184 J of energy to heat this much water.

Answer 1

Ignore the confusing stuff and you are left with:

required number of photons contain 4.184 J

So you need energy per photon, so that you can use

number of photons x energy per photon (J) = total photon energy = (in this case) 4.184J

To get energy per photon, use

E = Planck's constant x frequency.

So you need the frequency.

Use frequency x wavelength = speed for any wave motion, and

frequency (Hz, same as s-1) x 0.00300 m = 2.998 x 10^8 m s-1

in this example.

Now it's just arithmetic. Good luck!

Principles:

Separate out what is relevant. Write down the key equations to get you to where you want to be. See what else you need to know, and write out the key equations for that, until you get back to something you already know.

Does that help?

Answer 2

Nb = E/eb = 2500/(4.13E-15*299.79E6/419E-9) = 846.03 blue guys. Nr = E/er = 2500/(4.13E-15*299.78E6/689E-9) = 1391.25 red guys. The e's are e = hc/L in general. Are you using the eV.s consistent Planck's Constant and not the J.s one.