posted by kelsie on .
Enormous numbers of microwave photons are needed to warm macroscopic samples of matter. A portion of soup containing 177 g of water is heated in a microwave oven from 20degrees Celsius to 98 degrees Celsius, with readiation of wavelength 1.55x10^-2m. How many photons are absorbed by the water in the soup?
Calculate q for the heat required to heat the soup.
q = mass x specific heat H2O x delta T.
q = ?? in Joules.
Then use E = hc/wavelength to determine the energy per photon. Go from there. Post your work if you get stuck. Check my thinking.
ok. whew. just put in my answer into webassign and i got it correct.
Ill show the example with the numbers I was given. That way you can actually do the problem with your numbers.
I found the way to do this at the link below.
so my water mass was 360 g
my temp went from 28C to 93C
the radiation of wavelength is 1.55 x 10-2 m (same)
k so the first thing to do is find the work needed.
this is mass times (4.184J/g°C) ΔT. so (360)(4.184)(93-28) = 97905.6 J. The 4.184 changes things to Angstroms. The overall equation will have the units Joules.
k so we also have the equations
E'=hv and c=λv
h = 6.626 x 10^-34
c = 3 x 10^8
solve and replace so that somehow you get this
Q (97905.6 J) / (hc/1.55 x 10^-2)
I got 7.6e27
webassign verified it.
its so easy