HW 2 Q 5

[mya warner 2C]

Q:
How many photons with a wavelength of 885 nm are needed to melt 433 g of ice? The enthalpy of fusion of water can be found in this table.

I have tried many many times to get the correct solution for this problem but I can not get the right answer. Can someone please walk me thru the steps they took to get the right answer?

[Joanna Zhao 1J]

The enthalpy of fusion of water is 333.6 J/g. That means that to melt 433g of ice, you'd need a total of (333.6J/g)*(433g) Joules of energy. So, in order to solve the final solution of how many photons are required, the second step is to find out how much energy each photon carries. They gave me the photon's wavelength, so I used E = hc/lambda to solve for the energy per photon. Then, I divided the total energy needed (333.J/g * 433g) by the energy per photon to yield amount of photons needed.

If it helps at all, I look at the units to make sure I'm on the right path. The final calculation had units of Joules being divided by units of Joules/photon so I knew that the final answer represented how many photons were needed. I hope this was helpful!

[Alyssa Ly 2G]

Hello!

This problem requires you to use the equation E = h(frequency) and c = (wavelength)(frequency). To start, you can take the grams of ice given and then use the enthalpy of fusion of water given in order to get the amount of energy needed to melt that amount of ice.
(433g Ice) * (333.6J/1g) = 144448.8J

Then, using the two equations mentioned above, you can combine them to get the equation E = (hc)/(wavelength). Then, plug in all the given values to get the amount of energy per photon.
E = hc/wavelength = [(6.63 x 10^-34Js)(3 x 10^8 m/s)]/(885 x 10^-9m) = 2.25 x 10^-19 J/photon

(144448.8J)*(1 photon/2.25 x 10^-19J) = number of photons needed !!

Hope this helps! :)