Units for Einstein coefficients in stimulated emission?

  • #1

Homework Statement


I need to know the correct SI units for Einstein Coefficients (A and B) for stimulated emission (say laser).
The equation I'm on about is

Homework Equations

[tex]\frac{A}{B}[/tex] = [tex]\frac{8\pi h\nu^{3}}{c^{3}}[/tex]

The Attempt at a Solution

after some scribbling I got to [tex]\frac{A}{B}[/tex] = [tex]\frac{Js}{m^{3}}[/tex]
where J is joules, s seconds and m is meter.

any help appreciated. thanks
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  • #2
According to Wikipedia, the units of A are radians per second, and based on the ratio you got you should be able to figure out what the units of B are. Although I'm not sure whether to trust Wikipedia on this without having some other source (i.e. a textbook) to back it up.
  • #3
thanks for your reply diazona!

apparently A is the probability per unit time of an electron making spotaneous transition so assuming A to be [tex]s^{-1}[/tex] then B should be [tex]\frac {m^{3}}{Js^{2}}[/tex], http://en.wikipedia.org/wiki/Einstein_coefficients#The_Einstein_coefficients" gives for B [tex]\frac {sr m^{2}}{Js}[/tex] where sr is solid angle and is dimensionless. I'm getting close but what am i doing wrong??
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  • #4
Wikipedia's right, I just happened to be working on this so let me show you why.

The units of coefficient A has the same units as BxJ, where J is the average specific intensity with units Jm-2s-1Hz-1Sr-1

A is the transition probability so has unit s-1

After juggling around I get =(m2SrHz)/J = what Wikipedia says :)
  • #5
Sorry to dig up this old thread, but I came across this post when trying to find out which units to use and thought I should add the correct answer now I've found it.

Radiative Processes in Astrophysics by Rybicki and Lightman (p29) defines the transition probability per unit time ([itex]\mathrm{s}^{-1}[/itex]) for stimulated emission as [itex]B_{21}\overline{J}[/itex], where [itex]\overline{J}[/itex] is the mean intensity ([itex]\mathrm{Jm^{-2}s^{-1}sr^{-1}Hz^{-1}}[/itex]). This gives [itex]B_{21}[/itex] in units of [tex]\mathrm{m^2 sr J^{-1} s^{-1}}[/tex] However, the book also states that the energy density [itex]u_\nu[/itex] is often used instead of [itex]J_\nu[/itex] to define the Einstein B-coefficients. [tex]u_\nu=\frac{4\pi}{c}J_\nu[/tex] where [itex]J_\nu[/itex] is in the same units as [itex]\overline{J}[/itex] and therefore the units of [itex]u_\nu[/itex] are [itex]\mathrm{Jm^{-3}sr^{-1}Hz^{-1}}[/itex]. Therefore if the transition probability is defined as [itex]B_{21}\overline{u}[/itex] (with [itex]\overline{u}[/itex] again in the same units as [itex]u_\nu[/itex]) then the units of [itex]B_{21}[/itex] become [tex]\mathrm{m^3 sr J^{-1} s^{-2}}[/tex] So both of you were correct! Just make sure you stick to one definition or the other.
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1. What are Einstein coefficients in stimulated emission?

Einstein coefficients are numerical values that describe the probability of an atom undergoing stimulated emission, which is a process where an incoming photon causes an excited atom to emit another photon with the same energy, direction, and phase.

2. What units are used to measure Einstein coefficients in stimulated emission?

The units used for Einstein coefficients in stimulated emission are inverse seconds (s-1). This represents the rate at which stimulated emission occurs.

3. How are Einstein coefficients related to the properties of a material?

Einstein coefficients are related to the properties of a material through the atomic transition probability, which is determined by factors such as the energy levels of the atoms and the density of the material.

4. What is the significance of Einstein coefficients in stimulated emission?

Einstein coefficients are significant because they provide a quantitative way to describe stimulated emission, which is a key process in the operation of lasers and other optical devices.

5. How are Einstein coefficients experimentally determined?

Einstein coefficients can be experimentally determined by measuring the intensity of light emitted from a material under different conditions, and then using mathematical equations to calculate the coefficients based on the observed data.

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