College: Chemistry
posted by Mai .
Hi there, I need help on my homework for chemistry and I do not understand the step on how to work this problem out. Please help me with this problem:
On a Sunday morning while having your breakfast you determine that you need about 2.95X10^(5)J to heat water for your tea in the microwave. If 2.5X10^(24) photons hit the cup every second and you set the timer to 2.4 min, what should the frequency of the microwave be so that the tea is ready in that time?

•Convert the minutes to seconds.
•Multiply (photons/sec) by number of seconds to get the total number of photons.
•Divide total joules by numer of photons to get the energy of a photon.
• E(photon) = h*f (f = freq.)
Substitute E and h into the above formula and solve for f. 
2.4 min x (60s/1min) x 2.5 x 10^24 photons/s = 3.6 x 10^26 photons
energy per photon = 2.95 x 10^5 J/3.6 x 10^26 photon = 8.2 x 10^22 J/photon
Now, E = hf
f = E/h
f = 8.2 x 10^22 J/6.626 x 10^34 J.s
f = 1.2 x 10^12 s^1
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