You need 14 kW of infrared laser light power with wavelength 1270 nm to bore a hole in a diamond. How many downward atomic transitions per second...

We know how much energy we need altogether: 14 kilowatts. So all we need to do is figure out the energy of each transition, and then that will tell us how many transitions we need.

The energy of the photon emitted by the transition is given by its wavelength according to this equation:

`E = {h c}/lambda `

Plug that in, and we have:

`E = (6.626 * 10^-34 J * s)(3.00 * 10^8 m/s)/(1.270 *10^-9 m) = 1.565*10^-16 J`

So now, we just divide that into 14 kW:

`(1.4*10^4 W)/(1.565*10^-16 J) = 8.946*10^19 s^{-1}`

So we need `8.946*10^19` atomic transitions per second.