Stimulated emission per second per atom?

In summary, the conversation discusses the calculation of the probability per atom and second for stimulated emission from 2p to 1s in a plasma with the temperature of 4500 ºC. This involves using Plank's radiation law and Einstein coefficients to find the rate of stimulated emission per atom per second. The units of the coefficient on the upper state population density must be ##s^-1##.
  • #1
Philip Land
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3

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


Planks radiation law:
##\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?
 
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  • #2
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?
 
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  • #3
Cutter Ketch said:
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.
 
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Related to Stimulated emission per second per atom?

1. What is stimulated emission per second per atom?

Stimulated emission per second per atom is a measure of the rate at which atoms emit photons due to the stimulation of surrounding photons. It is a key concept in the field of quantum optics and is important for understanding the behavior of lasers and other light-emitting devices.

2. How is stimulated emission per second per atom related to population inversion?

Stimulated emission per second per atom is closely related to population inversion, which is the condition in which there are more atoms in an excited state than in a lower energy state. This is necessary for stimulated emission to occur and for a laser to produce a coherent beam of light.

3. What is the difference between stimulated emission and spontaneous emission?

Stimulated emission involves the release of photons from an excited atom due to the presence of surrounding photons, while spontaneous emission is the random emission of photons from an excited atom without the presence of external stimuli. Stimulated emission results in a coherent beam of light, while spontaneous emission produces light in all directions.

4. How does stimulated emission per second per atom affect the intensity of a laser beam?

Stimulated emission per second per atom is directly proportional to the intensity of a laser beam. This means that the more stimulated emissions that occur per second per atom, the higher the intensity of the laser beam will be. This relationship is described by the Einstein coefficients.

5. Can stimulated emission per second per atom be controlled?

Yes, stimulated emission per second per atom can be controlled through various methods such as adjusting the energy levels of the atoms, controlling the intensity of the stimulating photons, and manipulating the size and shape of the laser cavity. This control allows for precise tuning of the laser output and is crucial for many applications such as in medicine, telecommunications, and scientific research.

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