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. Determine the distance travelled by the free electron in 1 s , assuming no collisions occur.

Step-by-step solution

The force experienced by the electron in the electric field is given by F = eE . The acceleration of the electron is a = eE m . Using the equation of motion s = ut + 1 2 at^2 with initial velocity u = 0 , the distance travelled is: s = 1 2 ( eE m ) t^2 Substituting the standard values e = 1.6 10⁻¹⁹ C , m = 9.1 10⁻³¹ kg , and the given values E = 5.0 10^3 V m ⁻¹ , t = 10⁻⁶ s : s = 1 2 1.6 10⁻¹⁹ 5.0 10^3 9.1 10⁻³¹ (10⁻⁶)^2 s = 1 2 8.0 10⁻¹⁶ 9.1 10⁻³¹ 10⁻¹² s = 4.0 9.1 10^3 s = 4000 9.1 439.56 m Rounding to the neares