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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 exists in the vicinity of the event. (a) Find the distance travelled by the free electron in 1 μs 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.

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 exists in the vicinity of the event. (a) Find the distance travelled by the free electron in 1 μs 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.

Grade:upto college level

1 Answers

Jitender Pal
askIITians Faculty 365 Points
6 years ago
Sol. E = 5 Kv/m = 5 * 10^3 v/m ; t = 1 μs = 1 * 10^–6 s F = qE = 1.6 * 10^–9 * 5 * 10^3 A = qE/m = 1.6 *5 *10^-6/9.1 *10^-31 a) S = distance travelled = 1/2 at^2 = 439.56 m = 440 m b) d = 1 mm = 1 * 10^-3 m 1 * 10^-3 = 1/2 * 1.6 * 5/9.1 10^5 * t^2 ⇒ t^2 = 9.1/0.8 * 5 * 10^-18 ⇒ t = 1.508 * 10^-9 sec ⇒ 1.5 ns.

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