Question

How many photons are produced in a laser pulse of 0.497 J at 469 nm?

Answer 1

Answer:

$1.1702\times 10^{18}$photons are produced in a laser pulse of 0.497 Joules at 469 nm.

Explanation:

Energy of the laser pulse ,E'= 0.497 J

Number of photons = n

Energy of 1 photon with 469 nm wavelength = E

E' = n × E

$E=\frac{hc}{\lambda }$

h = Planck's constant = $6.626\times 10^{-34}Js$

c = speed of light = $3\times 10^8m/s$

$\lambda$ = wavelength = $469 nm=469\times 10^{-9}m$

$1 nm=10^{-9} m$

Now put all the given values in the above formula, we get the energy of the photons.

$E=\frac{6.626\times 10^{-34}Js\times 3\times 10^8m/s}{469\times 10^{-9}m}=4.2384\times 10^{-19} J$

$n=\frac{E'}{E}$

$n=\frac{0.496 J}{4.2384\times 10^{-19} J}=1.1702\times 10^{18} photons$

$1.1702\times 10^{18}$photons are produced in a laser pulse of 0.497 Joules at 469 nm.

Answer 2

E=hν where E is the energy of a single photon, and ν is the frequency of a single photon. We recall that a photon traveling at the speed of light c and a frequency ν will have a wavelength λ given by λ=cνλ will have an energy given by E=hcλλ=657 nm. This will be E=(6.626×10−34)(2.998×108)(657×10−9)=3.0235×10−19J So we now know the energy of one photon of wavelength 657 nm. To find out how many photons are in a laser pulse of 0.363 Joules, we simply divide the pulse energy by the photon energy or N=Epulse Ephoton=0.3633.0235×10−19=1.2×1018So there would be 1.2×1018 photons of wavelength 657 nm in a pulse of laser light of energy 0.363 Joules.