A microwave oven heats by radiating food with microwave radiation, which is absorbed by the food and converted to heat. Suppose an oven’s radiation wavelength
is 12.5 cm. A container with 0.250 L of water was placed in the oven, and the
temperature of the water rose from 20.0°C to 100.0°C. How many photons of this
microwave radiation were required? Assume that all the energy from the radiation was
used to raise the temperature of the water.

5.283x10^28

Explanation:

Each photon emits an energy of hf, where f is the frequency and h being planck's constant.

The heat required to raise the temperature of water from 20°C to 100°C is

Q = mS(dT)

= (density of water)(volume of water)(4200J/K)(80K)

= (10^3 kg/m^3)(0.25x10^-3 m^3)(4200J)(80)

= 84000J

Energy of each photon having wavelength 12.5x10^-2 m is

(6.62x10^-34)((3x10^8)/(12.5x10^-2)) = 1.59x10^-24J

Thus, the number of photons required are 84000/(1.59x10^-24)

= 5.2830x10^28.

Hope the explanation is sufficient.