Probability per atom and per second for stimulated emission to occur

  • #1

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


[/B]
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?
 

Answers and Replies

  • #2
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The probability of stimulated emission will depend on the density of radiation around the atom, which depends on the temperature.
 
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  • #3
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).
 
  • #4
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Did you use the given lifetime already?
 
  • #5
Did you use the given lifetime already?
Yes I used that to get the frequency, used in Plancks radiation law.
 
  • #6
TSny
Homework Helper
Gold Member
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##A_{21} = \rho (f) * \frac{N_1}{N_2}*B_{12} -B{21}*\rho (f). ##
It might help to rearrange this equation as ##N_2A_{21} + N_2B_{21}\rho (f)= N_1B_{12}\rho (f) ##.
Interpret each of the terms. One of the terms is closely related to what you are asked to find.
 

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