Need help on reveiw problem for chemists only, got answer but not sure if its right.?

Question

the question:
How many photons of wavelength 4.00 nm are required to heat 250.0 g of water from fuacet temperature of 10.6 C to 100.0C without boiling? asume all radiation is used to heat the water.

I figured that when it says by photons it meant waves becuase theres no equation which tells a number of photons. I first figured how much Kcals(1000 caloiries) were needed to heat the water, then how much Kcals where released through each 4.00nm wave of radiation. Then of course I divided them to figure out how many waves where need, but it came out to be an extremely small number.

My answer: 3.13 x (10 ^-3) , this answer i am not sure if i did it right like i could be wrong about how I came to solve it. I also redid it in Joules and came out to the same answer, but still it could be the way I did it.

So if you see a mistake in the way I did it, or show me how to do it, it would be helpful in my reveiw.

Answer 1

Ok. First find the heat needed.
Q = mcΔT = 0.25 x 4200 x 89.4 = 93870 J
Now remember the quantized energy equation E = nhf
n = E/hf = Eλ/hc = 93870 x 4E-9 / (6.63E-34 x 3E8) = 1.888E21