A container with 0.293 L of water is placed into microwave and is then radiated with electromagnetic energy that has a wavelength of 12.9 cm. The temperature of the water then rose by 78.7 degrees Celsius. Calculate the number of photons that were absorbed by the water. Assume the water has a density of 1.00 g/mL and its specific heat is 4.184 J/g*C.

Question

edliu95 · Answer

0.293 L = 293 mL (H2O 1.00 g/mL) = 293 g H2O
E = q = (293 g H2O)(4.184 J/g*C) (78.7) = 96479.3 J

(12.9 cm/1) (1 m/100 cm) ( 1 nm / 1.0 x10^-9 m) = 0.129 x 10^-9
C ("Speed of Light") = (lambda)(frequency) ==> C/(lambda) = (frequency)
==> (2.998x10^8)/(0.129x10^-9) = 2.324x10^18

E1 ("Energy per Photon") = h ("Planck's Constant") x frequency
E1 = (6.626x10^-34)(2.324x10^18) = 1.5399x10^-15 

Tried (96479.3 J)/(1.5399x10^-15) = 6.265x10^19, but wasn't correct.

anonymous · Answer

The wavelength of the wave = 12.9 cm. Why do you convert it to nm?

edliu95 · Answer

Never mind, I got assistance from an on campus tutor and saw my error, the conversion to nm was the error, since the speed of light is measured in m/s, converting it to nm turned it to nm/s, throwing off the process for calculating E per photon.

Revised Work:
(12.9 cm/1) (1 m/ 100 cm) = 0.129 m
(2.998x10^ 8 m/s)/(0.129 m) =2.324x10^9 1/s
(6.626x10^-34)(2.324x10^9) =1.5399x10^-24 = E per photon
96479.3 J / 1.5399x10^-24 = 6.265x10^28 photons

I accidentally converted to nm since normally we are given wavelengths in nm which we have to convert to m, and somewhere in the process, mindlessly thought it had to be something B x10^-9 which resulted in the wrong answer I got earlier.

anonymous · Answer

That's cool