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

Question

Chemistry

Georgia Ryan

22 June, 09:26

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

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Alice Hartman · 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