Question

A container with 0.413 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 76.5 °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

Answer 1

Mass of water = density x volume
Mass of water = 0.413 x 1
Mass of water = 0.413 g

Energy absorbed = mCpΔT
Energy = 0.413 x 4.184 x 76.5
Energy = 132.2 J

Using Planck's equation:
E = nhc/λ
132.2 = (n x 6.63 x 10⁻³⁴ x 3 x 10⁸) / (13.3 x 10⁻²)

n = 8.84 x 10²⁵ photons