Question

A molecule of a gas, filled in a discharge tube, gets ionized when an electron is detached from it. An electric field of $5.0kV{m}^{-1}$ exists in the vicinity of the event (a) Find the distance travelled by the free electron in 1 \mu s assuming no collision. (b) If the mean free path of the electron is 1.0 mm, estimate the time fo transit of the free electron between successie collision.

Answer 1

Given, $E=kv/m=m=5\times {10}^{3}v/mt=1\mu S=1\times {10}^{-6}sF=qE=1.6\times {10}^{-19}\times 5\times {10}^3$
$a=\frac{qE}{m}=\frac{1.6\times 5\times {10}^{-16}}{9.1\times {10}^{-31}}$
(a) S = Distance travelled
$=\frac{1}{2}a{t}^2=\frac{1}{2}\times \frac{1.6\times 5}{9.1}\times {10}^{-16+31}\times ({10}^{-6}{)}^2=\frac{1}{2}\times \frac{1.6\times 5}{9.1}\times {10}^{15}\times {10}^{-12}=0.43956\times {10}^{3}m=439.56m=440m(b)d=1mm=1\times {10}^{-3}m1\times {10}^{-3}=\frac{1}{2}\times \frac{1.6\times 5}{9.1}\times {10}^{15}\times (t{)}^2\Rightarrow t^2=\frac{2\times 9.1\times {10}^{-3}}{1.6\times 5\times {10}^{15}}\Rightarrow t^2=\frac{9.1}{0.8\times 5}\times {10}^{-18}\Rightarrow t=1.508\times {10}^{-9}sec.=1.5ns.$