Question

Quantum Theory Problem
How many photons at 660 nm must be absorbed to melt 5.00 x 102 g of ice at 0oC? On average, how many water molecules does one photon covert from ice to water (at 0oC)? Note: it takes 334 J to melt 1 g of ice at its freezing point.

Answer 1

assuming all the photons are absorbed....
heat required to melt ice = energy of all the photons... right?
4.0x10^2 g x 334 J/g = energy of photons.
1.34x10^5 J = energy of photons. ok?

*** 2 ***
then...for a single photon...
E = hc/L = 6.626x10^-34 J s x (3.00x10^8 m/s) / (660 nm x 1m/10^9nm) = 3.01x10^-19 J

ie... 3.01x10^-19 J/photon...

1.34x10^5 J x (1 photon / 3.01x10^-19J) = 4.4x10^23 photons



4.0x10^2 g x (1 mole / 18.0g) x (6.022x10^23 molecules / mole) = 1.34x10^25 molecules of water

1.34x10^25 molecules of water / 4.4x10^23 photons = 30 molecules of water per photon