- #1

warhammer

- 151

- 31

- Homework Statement
- The distribution of free path is given as N = N(o) e^ (-x/lambda) where lambda is the mean free path, and N is the number of molecules that survive collision on travelling a distance x, and N(o)is the no. of molecules at distance x = 0. Show that the root mean square (rms) free path is given by √2*lambda

- Relevant Equations
- lambda (rms)= v(rms) * t(rms) where t(rms) is the relaxation time.

lambda (rms)= v(rms) * t(rms) -- 1

Now I assume here that t(rms)=1/(√2*n*π*d^2*v(rms))

But this cancels the v(rms) term when used in eq (1) so the mean free path and the RMS free path would actually be the same (even later on when used in the aforementioned Survival Equation)

I would like to state that I have not understood what is meant by v(rms) clearly.. I would be really obliged if someone would explain the concept behind the question as well as provide the guidance to complete the question.

(I even tried to use the original derivation that was used for Survival Eqn in context of Maxwellian gas but that also provided no real insight)

Now I assume here that t(rms)=1/(√2*n*π*d^2*v(rms))

But this cancels the v(rms) term when used in eq (1) so the mean free path and the RMS free path would actually be the same (even later on when used in the aforementioned Survival Equation)

I would like to state that I have not understood what is meant by v(rms) clearly.. I would be really obliged if someone would explain the concept behind the question as well as provide the guidance to complete the question.

(I even tried to use the original derivation that was used for Survival Eqn in context of Maxwellian gas but that also provided no real insight)