How many photons are in a laser pulse of 0.363J at 657 nm?

Question

anonymous · Answer

The way to work this out is by using the relation $$E=h\nu$$ where E is teh energy of a single photon, and $\nu$ is the frequency of a single photon.  We recall that a photon traveling at the speed of light $c$ and a frequency $\nu$ will have a wavelength $\lambda$ given by $$\lambda=\frac{c}{\nu}$$.  We can combine this equation with the energy relation equation above to find that a photon with a wavelength $\lambda$ will have an energy given by $$E=\frac{hc}{\lambda}$$We can now calculate the energy of a single photon of wavelength $\lambda=657$ nm.  This will be $$E=\frac{(6.626\times10^{-34})(2.998\times10^{8})}{(657\times10^{-9})}=3.0235\times10^{-19}\rm{J}$$
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 $$N=\frac{E_{pulse}}{E_{photon}}=\frac{0.363}{3.0235\times10^{-19}}=1.2\times10^{18}$$So there would be $1.2\times10^{18}$ photons of wavelength 657 nm in a pulse of laser light of energy 0.363 Joules.