Helium at a low pressure is contained within a discharge tube. A large potential difference is applied across this tube. Consider a helium atom that has just been ionized by the detachment of an atomic electron. Determine the ratio of the distance travelled by the free electron to that by the positive ion in a short time interval dt following the ionization.

Step-by-step solution

Let E be the electric field applied across the discharge tube. The force on the free electron is F_e = eE , and its acceleration is a_e = eE m_e . Since the helium atom is ionized by the detachment of a single electron, the charge on the helium ion (He ^+ ) is +e . The force on the helium ion is F_i = eE , and its acceleration is a_i = eE m_i . The distance travelled by a particle starting from rest in a short time interval dt is given by s = 1 2 a(dt)^2 . The ratio of the distances travelled by the electron and th