Chemistry - Photons

Water is exposed to infrared radiation of wavelength 2.5×10−4 cm. Assume that all the radiation is absorbed and converted to heat.

How many photons will be required to raise the temperature of 2.5 g of water by 2.5 K?

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I tried solving this problem on my own, and I got 3.3 x 10^-30 photons, which was incorrect.

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asked by Amy
  1. I worked this earlier. If you will show exactly what you did from my workup perhaps I can figure out what's wrong.

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    posted by DrBob222
  2. 2.5g x 4.184J/g*K x 2.5K = 26.15 J
    E= 6.626E-34 J.s x 3E8 m/2.4E-6 m = 8.285 E-32
    26.15/8.285E-32 = 3.15E-32 - incorrect answer

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    posted by Amy
  3. 2.5g x 4.184J/g*K x 2.5K = 26.15 J
    First step is ok.

    E= 6.626E-34 J.s x 3E8 m/2.4E-6 m = 8.285 E-32
    The numbers are ok that you substituted but the answer is 8.2825E-20 J. That't too many significant figure but I'll round at the end.

    26.15/8.285E-32 = 3.15E-32 - incorrect answer
    3.157E20

    That catches two errors in two steps. I suspect, also, that you are reporting too many significant figures. I would round to 2 places since the 2.4, 2.5 and 2.5 limits it to two s.f. So I round round to 3.2E20
    You may also want to check the problem. You have 2.5E-4 cm in the problem but used 2.4 in the work. I think I remember the number from your first post, however, as being 2.4E-4 cm wavelength.

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    posted by DrBob222
  4. I did get the correct answer. It was actually 3.29E-20. Thank you for your help.

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    posted by Amy
  5. I can't buy into 3.29E-20. 3.29E+20 might be ok but certainly not -20. A photon of 2.4E-6 meters is 8.28E-20 J and
    8.28E-20 J/photon x 3.29E-20 photons provides 2.72E-39 which doesn't come close to providing enough energy to heat 2.5 g H2O by 2.5K.

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    posted by DrBob222

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