Week 2 Homework Sapling #7

[Melanie Krahn 1C]

Hi all. I've been having difficultiess solving this problem. I'd love to see how someone worked it out. Thanks!

How many photons with a wavelength of 769 nm are needed to melt 469 g of ice? The enthalpy of fusion of water can be found in this table.

[TiffanyBrownfield 2I]

First you would need to calculate the energy of a photon with that wavelength. You would use the equation E(proton)= hc/λ (which is derived from the equation E=hv). So in this case it would be
E= (6.626 x 10^-34 Js) x (3x10^8m/s)/(769 x 10^-9).
E= 2.5849 x 10^19
This is the energy per one photon.
If I remember correctly the enthalpy of fusion for water is 333.6 J/g. Since this is the energy required for only one gram, you would have to multiply this by how many grams are given (in this case 469g).
(333.6 J/g) x (469g) = 156458.4 J.
This being the energy required to melt 469 grams.
Then you would simply divide the energy required (156458.4 J) by the energy per photon (2.5849 x 10^-19) to get your answer.
If my calculations are correct it should be around 6.05 x 10^23 photons.

[LarisaAssadourian2K]

Hello! To solve this problem, you first plug in the 769nm into the equation E=(hc)/ λ to solve for the amount of energy needed for a photon. Next, use the information from the table provided to convert the number of grams of ice to joules for the enthalpy of fusion. Lastly, divide E(photon)/joules of H20 and you should have your answer. I hope this helps!

[Natalie Do 3F]

Remember that enthalpy of fusion refers to the heat of the system which in this case is the number you are looking for for the ice to melt.

[Jose Miguel Conste 3H]

First find the frequency using the c=lambda times frequency equation, then find the energy when the frequency is found using the E=hv equation, then with the number of grams of ice, multiply it times the enthalpy of fusion; then with the energy found divide the answer multiplied with grams of ice and enthalpy by the energy you found earlier to get the answer

[Jack_Pearce_2H]

use the enthalpy to find the joules required to melt the ice, solve for the energy per photon using the given wavelength and then divide the energy required to melt thr ice by the energy per photon to find how many photons are required