# Stimulated emission per second per atom?

## Homework Statement

We are investigating hydrogen in a plasma with the temperature 4500 ºC. Calculate the probability per atom and second for stimulated emission from 2p to 1s if the lifetime of 2p is 1.6 ns

## Homework Equations

##\rho (f) = \frac{8* \pi h}{c^3}\frac{1}{e^{\frac{hf}{kT}} -1}## (1)

Einstein coefficients :
##A=\frac{8 \pi f^3 h}{c^3} B## (2)

## The Attempt at a Solution

I can take the inverse of the life-time to get A. Then I can just solve for B. Using that ##\lambda = 1.251*10^{-7}## (which I looked up).

I seek a unit that is per second per atom. Which I can't really get my head around.

I try to play around with the frequency density (1) but fail to find per atom. When I get "per atom" I can just multiply that with A.

Any tipps here?

Finding B as you describe is fine. Planck’s radiation law which you show will also be necessary. You are almost there. What is B good for? How is it used? Do you perhaps see it in a differential equation relating the rate of stimulated emission to the upper state population density? What must be the units of the coefficient on the upper state population density?

• Philip Land
Finding B as you describe is fine. Planck’s radiation law which you show will also be necessary. You are almost there. What is B good for? How is it used? Do you perhaps see it in a differential equation relating the rate of stimulated emission to the upper state population density? What must be the units of the coefficient on the upper state population density?
Thank you!

I figured out how to solve this. I wanted the unit ##s^-1##. (Which also A gave so i'm not sure I undertand the theory here). But evaluating the units I see that if I multiply B (which I can get if I know ##f##, which I can get from the Bohr model) by the frequency density I get the rate of stimulated emission per atom per second. So ##B * \rho ## is what I was seeking.

• Cutter Ketch