# Probability per atom and per second for stimulated emission to occur

## 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

##A=\frac{1}{\Sigma \tau}##

$$A_{2,1} = \frac{8*\pi *h * f^3*B_{2,1}}{c^3}$$

## The Attempt at a Solution

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hmmm, I'm not sure how to approach this problem. I took the inverse of the life time and got that A= ##6.25*10^8 S^{-1}.##

But I'm not sure where to start or what formulas to use.

The only formula I know of which takes temperature into account is
Doppler line width: ##\Delta F = constant * f_0 * \sqrt(T/M) ## which I can't see how to apply in this case at all.

Any input on where to start?

mfb
Mentor
The probability of stimulated emission will depend on the density of radiation around the atom, which depends on the temperature.

• Philip Land
The probability of stimulated emission will depend on the density of radiation around the atom, which depends on the temperature.

Thanks a lot! I manage to as you said find a relation between radiation density and temperature, (Planck’s radiation law).

Then I used a Radiation balance and solved for ##A_{21} = \rho (f) * \frac{N_1}{N_2}*B_{12}
-B{21}*\rho (f). ##

Where ##g_1*B_{12} = g_2*B_{21}## if we let g1=g2 we get ##B_{12}=B_{21}##

We also know from statistics that ##\frac{N_1}{N_2}= e^\frac{- \Delta E}{kT}##

But my question is. To get A (which I guess i'm supposed to get). I need B and ##\Delta E## But I don't have those quantities... (as i'm aware of).

mfb
Mentor