Question

A sodium lamp emits light at the power P = 90.0 W and at the wavelength λ = 597 nm, and the emission is uniformly in all directions. (a) At what rate are photons emitted by the lamp? (b) At what distance from the lamp will a totally absorbing screen absorb photons at the rate of 1.00 photon /cm2s? (c) What is the rate per square meter at which photons are intercepted by a screen at a distance of 1.30 m from the lamp?

Answer 1

power= 90 W

wavelength of photon= = 597 nm = 597 x10^-9 m

(a) Let n be the number of photons per second

n h c/ = 90 => n= 90 /hc

n= (90)(597 x10^-9) /(6.6 x10^-34 * 3x10⁸ m/s)

n= 2.71 x10²⁰ per second

so rate of photon emission= 2.71 x10²⁰ per second

(b) rate of absorption= 1 photon /cm² s

ler r be the distance from the lamp

so 2.71 x10²⁰ /( 4 pi r²) = 1 => r= (2.71 x10²⁰⁾/4 pi

r= 4.65 x10⁹ cm = 4.65 x10⁷ meter

(c) distance from lamp= 1.30 m

rate of photon emmision from lamp=   n= 2.71 x10²⁰ per second

so rate per square meter = n/ (4 pi r²) = 2.71 x10²⁰ /(4*3.14* 1.30²)

rate at which photons are intercepted = 1.277x10¹⁹ photons/m² s