Question #699d2
1 Answer
Explanation:
The first thing that you need to do here is to find the energy of a single photon of wavelength
#23.9color(white)(.)mu"m" = 23.9 * 10^(-6)color(white)(.)"m"#
As you know, the energy of a photon can be expressed in terms of its wavelength by using a version of the Planck - Einstein relation, which looks like this
#E =h * c/(lamda)#
Here
#E# is the energy of the photon#h# is Planck's constant, equal to#6.626 * 10^(-34)"J s"# #c# is the speed of light in a vacuum, usually given as#3 * 10^8"m s"^(-1)# #lamda# is the wavelength of the wave
Plug in your value to get
#E = 6.626 * 10^(-34)"J" color(red)(cancel(color(black)("s"))) * (3 * 10^8color(red)(cancel(color(black)("m"))) color(red)(cancel(color(black)("s"^(-1)))))/(23.9 * 10^(-6)color(red)(cancel(color(black)("m"))))#
#E = 8.317 * 10^(-21)color(white)(.)"J"#
Next, calculate the number of photons needed to get a total energy output of
#"485 kJ" = 485 * 10^3color(white)(.)"J"#
You will end up with
#485 * 10^3 color(red)(cancel(color(black)("J"))) * "1 photon"/(8.317 * 10^(-21)color(red)(cancel(color(black)("J")))) = 5.831 * 10^(25)color(white)(.)"photons"#
Finally, to convert the number of photons to moles, use Avogadro's constant, which tells you that in order to have
#5.831 * 10^(25)color(red)(cancel(color(black)("photons"))) * "1 mole photons"/(6.022 * 10^(23)color(red)(cancel(color(black)("photons")))) = color(darkgreen)(ul(color(black)("96.8 moles photons")))#
The answer is rounded to three sig figs.