Question #0252a
1 Answer
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
#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 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.