Question

Question #0252a

Answer 1

`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.