How many photons are produced in a laser pulse of 0.338 J at 505 nm?

1 Answer
Jan 18, 2018

#8.59 * 10^(17)#

Explanation:

You can start by figuring out the energy of a single photon of wavelength #"505 nm" = 505 * 10^(-9)quad "m"#.

To do that, use the equation

#E = h * c/(lamda)#

Here

  • #h# is Planck's constant, equal to #6.626 * 10^(-34)color(white)(.)"J s"#
  • #c# is the speed of light in a vacuum, usually given as #3 * 10^8color(white)(.)"m s"^(-1)#
  • #lamda# is the wavelength of the photon, expressed in meters

Plug in your value to find--notice that the wavelength of the photon must be expressed in meters in order for it to work here.

#E = 6.626 * 10^(-34)quad "J" color(red)(cancel(color(black)("s"))) * (3 * 10^8 color(red)(cancel(color(black)("m"))) color(red)(cancel(color(black)("s"^(-1)))))/(505 * 10^(-9)color(red)(cancel(color(black)("m"))))#

#E = 3.936 * 10^(-19) quad "J"#

So, you know that one photon of this wavelength has an energy of #3.936 * 10^(-19) quad "J"# and that your laser pulse produces a total of #"0.338 J"# of energy, so all that you need to do now is to find how many photons are needed to get the energy output given to you.

#0.338 color(red)(cancel(color(black)("J"))) * "1 photon"/(3.936 * 10^(-19) color(red)(cancel(color(black)("J")))) = color(darkgreen)(ul(color(black)(8.59 * 10^(17) quad "photons")))#

The answer is rounded to three sig figs.