InterviewSolution
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InterviewSolution
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The mean path length of alpha-particles in air under standard conditions is defined by the formula `R=0.98.10^(27)v_(0)^(3) cm`, this formula, find for an alpha-particle with initial kinetic enrgy `7.0 MeV`: (a) its mean path length, (b) the average number of ion pairs formed by the given alpha-particle over the whole path `R` as well as over its first half, assuning the ion pair formation energy to be equql to `34 eV`. |
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Answer» (a) For an alpha particle with initial `K.E 7.0 MeV`, the initial velocity is `V_(0)=sqrt((2T)/(M alpha))` `=sqrt(2xx7xx1.602xx10^(-6))/(4xx1.672xx10^(-24))` `= 1.83xx10^(9)cm//sec` Thus `R=6.02 cm` (b) Over the whole path the number of ion pairs is `(7xx10^(6))/(34)= 2.06xx10^(5)` Over the first half of the path:- We write the formula for the mean path as `R alphaE^(3//2)` where `E` is the initial energy. Thus if the energy of the `alpha` particle after traversing the first half of the path is `E_(1)` then `R_(0)E_(1)^(3//2)=(1)/(2)R_(0)E_(0)^(3//2) or E_(1)= 2^(-2//3)E_(0)` Hence number of ion pairs formed in the first half of the path length is `(E_(0)-E_(1))/(34eV)=(1-2^(-2//3))xx2.06xx10^(5)= 0.76xx10^(5)` |
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