Question

A photodiode sensor is used to measure the output of a 300W lamp kept 10m away. The sensor has an opening of 2cm in diameter. How many photons enter the sensor if the wavelength of light 600nm and the exposure time is 100ms .(Assume that all the energy of the lamp is given off as light and h=6.6times10^(-34)J-s

Answer 1

Energy of photon,

$E=hc/λ=6.62×10^{−34}×3×10^8/600×10^{−9}≈3.3×10^{−19}J$

The number of photons emitted per second,

$n=300/(3.3×10^{−19})=9.1×10^{20}s^{−1}$

The radiation is spherically symmetrical, the number of photons entering the sensor per second is the product of n and ratio of aperture area to the area of sphere of radius 10 m:

$(9.1×10^{20})(\pi×(0.01)^2)/(4×π×10^2)=2.3×10^{14} photon/second$

Therefore, number of photons entering the sensor in 0.1 s (or 100 ms)=$2.3*10^{14}*0.1=2.3*10^{13} photons$