Acontainer with 0.389 l of water is placed in a microwave and radiated with electromagnetic energy with a wavelength of 12.9 cm. the temperature of the water rose by 78.7 °c. calculate the number of photons that were absorbed by the water. assume water has a density of 1.00 g ⋅ ml − 1 and a specific heat of 4.184 j ⋅ g − 1 ⋅ ° c − 1 .

Explanation:

The given data is as follows.

       V = 0.389 L = 0.389 kg

        m = 389 g of water       (as 1 kg = 1000 g)

   wavelength = 12.9 cm

        dT =

First, we will identify the heat absorbed as follows.

            Q =

Putting the given values into the above formula as follows.        

          Q =

          Q =

               = 128090.231 J

Now, as we know that

            Energy (E) =

or,          

where,     h = Planck's Constant = J s

                c = speed of particle (i.e. light) = m/s

                E = energy per particle J/photon

Hence, calculate the energy as follows.

       E =

(As 1 m = 100 cm)          

         = J/photons

Hence, number of photons present will be calculated as follows.

   n photons =

                 =

                 =

                 =

Thus, we can conclude that number of photons released are .