Question

A heat lamp produces 22.0 watts of power at a wavelength of 6.8 μm . How many photons are emitted per second? (1 watt = 1 J/s). The answer needs to be in s^-1

Answer 1

Given the the power of lamp is 22.0 watt

22.0 watt = 22.0 watt x ( 1(J/s) / 1 watt ) = 22.0 J/s

We know that Energy, E = hc / λ

Where

h = plank's constant = 6.625x 10^-34 Js

c = speed of light = 3x 10⁸ m/s

λ = wave length = 6.8 μm = 6.8 x 10^-6 m                     Since 1 μm = 10^-6 m

Plug the values we get E = (6.625x 10^-34 Js x 3x 10⁸ m/s ) / (6.8 x 10^-6 m )

                                        = 2.92x10^-20 J/photon

Therefore the number of photons produced = [22.0 J/s ] x [ 1 photon / ( 2.92x10^-20 J)]

                                                                     = 7.5 x10²⁰

So the number of photons emitted is 7.5 x10²⁰ s^-1