Question

Question #699d2

Answer 1

`"96.8 moles"`

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 `1` mole of photons, you need `6.022 * 10^(23)` photons.

`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.