Acontainer with 0.317 l of water is placed into microwave and is then radiated with electromagnetic energy that has a wavelength of 13.3 cm. the temperature of the water then rose by 74.3 °c. calculate the number of photons that were absorbed by the water. assume water has a density of 1.00 g·ml–1 and its specific heat is 4.184 j·g–1·°c–1

The number of photons absorbed by the water is

Explanation:

where,

E = energy of the photon

h = Planck's constant  =

c = speed of light  =

= wavelength of photon  = 13.3 cm = 0.133 m   (Conversion factor:  1 m = 100 cm )

Putting values in above equation, we get:

To calculate the mass of water, we use the equation:

Density of water = 1 g/mL

Volume of water = 0.317 L = 317 mL     (Conversion factor:  1 L = 1000 mL )

Putting values in above equation, we get:

where,

q = heat absorbed

m = mass of water = 317 g

c = specific heat capacity of water = 4.184 J/g°C

= change in temperature = 74.3°C

Putting values in above equation, we get:

Putting values in above equation, we get:

Hence, the number of photons absorbed by the water is