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

• Philip Land
In summary: The other two are more general.The closely related term is the number of atoms in a particular region, which is what you are asked to find. The other two terms are the density of radiation and the heat capacity of a material.

## 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?

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

Philip Land
mfb said:
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 said:
Yes I used that to get the frequency, used in Plancks radiation law.

Philip Land said:
##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.

## 1. What is the concept of probability per atom and per second for stimulated emission to occur?

The concept of probability per atom and per second for stimulated emission to occur is a measure of the likelihood that an excited atom will release a photon of light due to the influence of a nearby photon. It is a fundamental concept in quantum mechanics and is essential for understanding processes such as laser operation.

## 2. How is the probability per atom and per second calculated for stimulated emission?

The probability per atom and per second for stimulated emission is calculated using the Einstein coefficients, which relate the rate of emission, absorption, and stimulated emission of photons by an atom. These coefficients take into account the energy levels of the atom and the number of photons present in the surrounding environment.

## 3. What factors can affect the probability per atom and per second for stimulated emission?

The probability per atom and per second for stimulated emission can be affected by several factors, including the energy levels of the atom, the intensity and frequency of the incident photon, and the temperature and pressure of the environment. Additionally, the presence of other atoms or molecules in the surroundings can also influence the probability of stimulated emission.

## 4. How does the probability per atom and per second for stimulated emission relate to the overall efficiency of a laser?

The probability per atom and per second for stimulated emission is a crucial factor in determining the overall efficiency of a laser. It represents the rate at which excited atoms release photons, which is essential for the amplification of light in the laser medium. Higher probabilities of stimulated emission lead to more efficient laser operation and stronger output beams.

## 5. Can the probability per atom and per second for stimulated emission be controlled or manipulated?

Yes, the probability per atom and per second for stimulated emission can be controlled and manipulated by adjusting the conditions of the laser medium. For example, by changing the energy levels of the atoms or the intensity and frequency of the incident photons, the probability of stimulated emission can be altered. This allows for fine-tuning of the laser's operation and performance.