A discharge tube contains helium at a low pressure. A large potential difference is applied across the tube. Consider a helium atom that has just been ionized due to the detachment of an atomic electron. Find the ratio of the distance travelled by the free electron to that by the positive ion a short time dt after the ionization.

Sol. Let the two particles have charge ‘q’ Mass of electron ma = 9.1 * 10^–31 kg Mass of proton mp = 1.67 * 10^–27 kg Electric field be E Force experienced by Electron = qE accln. = qE/m base e For time dt S base e = 1/2 * qE/m base e * dt^2 …(1) For the positive ion, Accln. = qE/4 * m base p S base p = 1/2 * qE/4 * m base p * dt^2 …(2) S base e/S base p = 4m base p/m base e = 7340.6