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

Explanation

Given, `E = Kv/m = 5 xx (10^3)v/m`,
` t = 1 mu S = 1 xx (10^-6)S `
` F = qE = 1.6 xx (10^-19) xx 5 xx (10^3)`
` a = qE/m = (1.6 xx 5 xx (10^-16))/(9.1 xx (10^-31))`
` (a) S = distance travelled `
` = 1/2 at^2 `
` = 1/2 xx ((1.6 xx 5)/9.1) xx (10^(-16+31)) xx ((10^-6)^2)`
` 1/2 xx ((1.6 xx 5)/9.1) xx (10^15) x (10^-12)`
` = 0.43956 xx (10^3) `
` = 439.56m = 440m.`