Question #0252a

1 Answer
Mar 25, 2017

#3.03 * 10^(20)"photons"#

Explanation:

The energy of a photon is directly proportional to its frequency, as described by the Planck - Einstein equation

#color(blue)(ul(color(black)(E = h * nu)))#

Here

  • #E# is the energy of the photon
  • #h# is Planck's constant, equal to #6.626 * 10^(-34)"J s"#
  • #nu# is the frequency of the photon

The first thing to do here is to figure out the energy of a single photon of frequency equal to #1.50 * 10^(14)"s"^(-1)#.

#E = 6.626 * 10^(-34)"J" color(red)(cancel(color(black)("s"))) * 1.50 * 10^(14)color(red)(cancel(color(black)("s"^(-1))))#

#E = 9.939 * 10^(-20)"J"#

You know that you need a total of #"30.1 J"# of energy, which means that you will need a total of

#30.1 color(red)(cancel(color(black)("J"))) * "1 photon"/(9.939 * 10^(-20)color(red)(cancel(color(black)("J")))) = color(darkgreen)(ul(color(black)(3.03 * 10^(20)color(white)(.)"photons")))#

The answer is rounded to three sig figs.