2014-07-31T19:30:38+05:30

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Mean free path is the distance traveled by a particle such as electron, in between two successive collisions.  It could be an atom, molecule in gases or liquids, or electrons in any medium or photons too.

l = 1 /  sigma * n
where sigma = effective cross sectional area offered by each particle, for collision
n = number of particles per unit volume = concentration of particles

One can prove this by estimating probability of a particle hitting or being stopped by collision in a small volume dV of area A & thickness dx:

From a beam many particles are travelling parallelly through a vertical slab of area A and thickness dx. In this volume we have n A dx number of particles.  Each particle has an effective surface area for collision = sigma. It is because only one side may be available for collision etc.  Total surface area of these that is available for collision is n A dx sigma. A particle that entered into this vertical slab of area A can encounter a surface area  n A dx sigma as obstruction or wall. So the expression for probability :
P (particle stopped or collision in volume dV) = n A dx  sigma / A  = n sigma dx

Now the Intensity I of a beam of particles is decreased by an amount dI.  dI is proportional to Intensity and the probability P.

dI  =  - I n sigma dx        -ve because intensity decreases due to collisions
dI / I  = -  n sigma  dx        In I = - n sigma x    =>  I(x) = I0  exp (- n sigma x)
I0 is I at x=0
Find the probability of a particle being stopped from x to x+dx. This is
P1(x) = [ I(x) - I(x+dx) ] / I0  =  (n sigma)  exp(-n sigma x)  dx

Expected value of x  is  Integral from 0 to infinity  of   x  * P1(x)
integral of x (n sigma) exp ( - n sigma x ) dx      =  1/n sigma
We call  1 / n * sigma = mean free path length = l

sorry i want the derivation
the above has a derivation. First we have probability of collision. Then we find the intensity of beam of particles. then we have probability of a particle at x being stopped in a volume dx. then we find average of x. This gives mean free path. Read the above you have the derviation.
ok thanks
2014-08-01T13:42:42+05:30
1=1/singma×n is a derication.HOPE IT HELPS...