Question

Estimate the number of photons emitted per second from 1.0 cm2 of a person's skin if a typical emitted photon has a wavelength of 10,000 nm. Assume the skin of a person is at the normal body temperature of 37∘C.

Answer 1

2.63 x 10^18

Step-by-step explanation:

A = 1 cm^2 = 1 x 10^-4 m^2

λ = 10,000 nm = 10,000 x 10^-9 m = 10^-5 m

T = 37 degree C = 37 + 273 = 310 k

Energy of each photon = h c / λ

where, h is the Plank's constant and c be the velocity of light

Energy of each photon = (6.63 x 10^-34 x 3 x 10^8) / 10^-5 = 1.989 x 10^-20 J

Energy radiated per unit time = σ A T^4

Where, σ is Stefan's constant

Energy radiated per unit time = 5.67 x 10^-8 x 10^-4 x 310^4 = 0.05236 J

Number of photons per second = Energy radiated per unit time / Energy of

each photon

Number of photons per second = 0.05236 / (1.989 x 10^-20) = 2.63 x 10^18