InterviewSolution
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InterviewSolution
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Let `alpha dt` be the probability of a sgas molecule experiencing a collision during the time interval `dt , alpha` is a constant. Find : (a) the probability of a molecule experiencing no collisions during the time interval `t` , (b) the mean time interval between successive collisions. |
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Answer» (a) Let `P(t)` = probability of no collision in the interval `(0, t)`, Then `P(t + dt) = P (t) (1 - alpha dt)` or `(dP)/(dT) = - alpha (t)` or `P (t) = e^(- alpha t)` where we have used `P(0) = 1` (b) The mean interval between collision is also the mean interval of no collision. Then `lt t gt = (int_0^oo te^(- alpha t) dt)/(int_0^oo e^(-alpha t)) = (1)/(alpha) (Gamma (2))/(Gamma(1)) = (1)/(alpha)`. |
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