How many photons are required for the liquid to absorb 34.86 J of heat?

Question

A liquid is exposed to infrared radiation with a wavelength of 6.86×10−4 cm. Assume that all the radiation is absorbed and converted to heat. How many photons are required for the liquid to absorb 34.86 J of heat?

Answer 1

The energy of one photon is given by Planck's equation E = hf where h is Planck's constant ( 6.63 x 10^-34 m² kg/s, and f is the photon frequency f = c/λ where c = 3.00 x 10⁸ m/s, λ = 6.86 x 10^-6 m.

E = 6.63 x 10^-34 x 3.00 x 10⁸ / 6.86 x 10^-6 = 2.90 x 10^-20 joules for one photon.

For a total energy of 34.86 j, there would be required 34.86 / 2.90 x 10^-20 = 1.20 x 10²¹ photons.

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