Question

A light beam of wavelength 5.6 * 10^-7 m, and intensity 53 W/m^2 shines on a target of area 3.6 m^2. How many photons per second are striking the target?

Answer 1

Let Area be S=3.6cm^2
Let Raditation be I= 53 W/m^2
Let Wavelength be L=5.6*10^-7m

1) The total power of light falling onto surface is
P=I*S (measured in Watts or Joules per second)

P=53 W/m^2*3.6*10^-4 m^2 =0.01908 W
2) The energy of a single photon is
E=hbar*w, where hbar is Planck const and w is angular frequency.
w=2*pi*c/L, where c is speed of light.

E=hbar*w =(h/2*pi)*2*pi*c/L=6.62*10^-34*(3*10^8/5.6*10^-7) =3.5464*10^-19 J
3) The number of photons per sec is total energy per sec div by energy of a single photon:
N=P/E=I*S*L/(2*pi*hbar*c) =5.38*10^16