How many photons are produced in a laser pulse of 0.401 J at 555 nm?
This question refers to a laser pulse, or electromagnetic radiation, with the wavelength of `lambda=` 555 nm ( 1 nanometer = 10^(-9) meter).
According to the quantum, or particle, theory of light, a laser pulse is an emission of a number of massless particles called photons. Each photon has the energy equal to
`E = hf` , where h is the Planck's constant:
`h = 6.626*10^(-34) J*s`
f is the frequency of the photon, or corresponding electromagnetic wave. The frequency and the wavelength are related as
`f = c/lambda` , where c is the speed of light: `c= 3*10^8 m/s` .
(Please see the "Planck's hypothesis" section of the reference website cited below.)
Then, if the pulse consists of N photons, its total energy would be
Then, for the pulse with the given wavelength and energy, we have
`NE = 0.401 J = N*6.626*10^(-34)J*s *((3*10^8) m/s)/(555*10^(-9) m)`
`N = 3.36*10^18` .
Approximately `3.36*10^18` photons are produced in the given laser pulse.