Question

How many photons are produced in a laser pulse of 0.338 J at 505 nm?

Answer 1

`8.59 * 10^(17)`

Explanation:

You can start by figuring out the energy of a single photon of wavelength `"505 nm" = 505 * 10^(-9)quad "m"`.

To do that, use the equation

`E = h * c/(lamda)`

Here

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

Plug in your value to find--notice that the wavelength of the photon must be expressed in meters in order for it to work here.

`E = 6.626 * 10^(-34)quad "J" color(red)(cancel(color(black)("s"))) * (3 * 10^8 color(red)(cancel(color(black)("m"))) color(red)(cancel(color(black)("s"^(-1)))))/(505 * 10^(-9)color(red)(cancel(color(black)("m"))))`

`E = 3.936 * 10^(-19) quad "J"`

So, you know that one photon of this wavelength has an energy of `3.936 * 10^(-19) quad "J"` and that your laser pulse produces a total of `"0.338 J"` of energy, so all that you need to do now is to find how many photons are needed to get the energy output given to you.

`0.338 color(red)(cancel(color(black)("J"))) * "1 photon"/(3.936 * 10^(-19) color(red)(cancel(color(black)("J")))) = color(darkgreen)(ul(color(black)(8.59 * 10^(17) quad "photons")))`

The answer is rounded to three sig figs.