How many photons are produced in a laser pulse of  0.401 J at 555 nm?

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ishpiro eNotes educator| Certified Educator

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 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 

`NE=Nhc/lambda` .

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)`

From here,

`N = 3.36*10^18` .

Approximately `3.36*10^18` photons are produced in the given laser pulse.

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