Question

How many photons are produced in a laser pulse of 0.258 j at 683 nm?

Answer 1

We can calculate the energy of a single photon through Plank-Einstein relation. We have


`E = hv`

where
`h` is the Plank's constant and
`v` is the frequency. Also, recall that to solve for the frequency, we have


`v = (c)/(\lambda)`

where
`c` is the speed of light and
`\lambda` is the wavelength of the laser, in meters. So for this problem we can compute for
`v` with


`v = (3.10^(8) m/s)/(683.10^(-9) m) \\ v = 4.39.10^(14)`

Going back to the Planck-Einstein relation, we have


`E = (6.626.10^(-34) J.s)(4.39.10^14 s^(-1))`

Hence, we have
`E = 2.91 x 10^(-19) J`.

Given that the laser emits an energy of 0.258 J, then there are


`number of photons = (0.258)/(2.91 x 10^(-19)) \\ number of photons = 7.5 x 10^(18)`.

Answer: 7.5 ⋅ 10^18 photons