Within a discharge tube filled with a gas, a molecule undergoes ionization, causing an electron to be detached. An electric field of 5.0 kV m ⁻¹ is present in the region of the event. Given that the mean free path of the electron is 1.0 mm , estimate the transit time of the free electron between successive collisions.

Step-by-step solution

The acceleration of the electron in the electric field is given by: a = eE m Assuming the electron starts from rest after being detached, the distance traveled between successive collisions is the mean free path . Using the equation of motion s = ut + 1 2 at^2 with u = 0 and s = : = 1 2 at^2 = 1 2 ( eE m ) t^2 Rearranging for the transit time t : t = 2m eE Substituting the given values ( E = 5.0 10^3 V m ⁻¹ , = 1.0 10⁻³ m , m = 9.1 10⁻³¹ kg , e = 1.6 10⁻¹⁹ C ): t = 2 9.1 10⁻³¹ 1.0 10⁻³ 1.6 10⁻¹⁹ 5.0 10^3 t = 18.2 1