Question

Question #ab3dc

Answer 1

`6.88 * 10^(17)`

Explanation:

Start by calculating the energy of a single photon of wavelength

`"563 nm" = 563 color(red)(cancel(color(black)("nm"))) * "1 m"/(10^9color(red)(cancel(color(black)("nm")))) = 5.63 * 10^(-7)color(white)(.)"m"`

To do that, you can use the Planck - Einstein relation, which tells you that the energy of a photon, `E`, is inversely proportional to its wavelength, `lamda`.

`E = h * c/(lamda)`

Here

• `h` is Planck's constant, equal to `6.626 * 10^(-34)color(white)(.)"J"`
• `c` is the speed of light in a vacuum, usually given as `3 * 10^8color(white)(.)"m s"^(-1)`

Plug in the value you have for the wavelength of the photon to get its energy--notice that I converted the wavelength to meters first!

`E = 6.626 * 10^(-34)color(white)(.)"J" color(red)(cancel(color(black)("s"))) * (3 * 10^8 color(red)(cancel(color(black)("m"))) color(red)(cancel(color(black)("s"^(-1)))))/(5.63 * 10^(-7)color(red)(cancel(color(black)("m"))))`

`E = 3.531 * 10^(-19)color(white)(.)"J"`

Now that you know the energy of a single photon of wavelength `"563 nm"`, you can use the total energy of the pulse to find the number of photons needed to produce it.

`0.243 color(red)(cancel(color(black)("J"))) * "1 photon"/(3.531 * 10^(-19)color(red)(cancel(color(black)("J")))) = color(darkgreen)(ul(color(black)(6.88 * 10^(17)color(white)(.)"photons")))`

The answer is rounded to three sig figs.