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 in a short time dt after the ionization.
Let the distance travelled by free electron and positive ion be SE and SH respectively. Also, mass of the electron and positive helium ion be me and mh where,
me=9.1×10-31kg
mh=4×mass of proton
=4×1.6×10-27kg
We know,
where s is the distance travelled, u is the initial velocity, t is the time and a is the magnitude of acceleration
Here, initial velocity of electron and helium ion is zero
∴
Now, magnitude of force experienced by electron,
where F is the magnitude of force, E is the electric field strength and q is the magnitude of charge of the particle.
∴ Distance travelled by free electron for dt duration is
Magnitude of force experienced by positive helium ion,
∴ Distance travelled by positive helium ion for dt duration is
The required ratio is
