Suppose an oven’s radiation wavelength is 0.125 m. A container with 300.00 g of water was placed in the oven, and the temperature of the water rose from 20.0°C to 80.0°C.

Question

How many photons of this microwave radiation were required to heat the water? (Assume that all the energy from the radiation was used to raise the temperature of the water.)

Answer 1

First, we'll find the energy of 1 photon at this wavelength, and then compute the total energy needed to change the temperature of the water. From that, we'll calculate the number of photons needed.

E = hν

c = λν

E = hc/λ

Finding the energy of a single photon:

E = energy of 1 photon = ?

h = Plank's constant = 6.626x10^-34 J-sec

c = speed of light =~3x10⁸ m/sec

λ = wavelength = 0.125 m

E = (3x10⁸ m/s)(6.626x10^-34 J-sec)(0.125 m) = 2.48x10^-26 J / photon

Total energy needed to raise temperature of 300.00 g water from 20 - 80C:

q = mC∆T

q = heat = ?

m = mass = 300 g

C = specific heat of water = 4.184 J/gº

∆T = change in temperature = 80 - 20 = 60ºC

q = (300 g)(4.184 J/gº)(60º) = 75,312 J = total energy needed

Calculation of number of protons needed:

75,312 J x 1 photon / 2.48x10^-26 J = 3.04x10³⁰ photons