When a charged particle of charge x C moves through a potential difference of y V, the gain in kinetic energy is equal to xy J.
An electron and an alpha particle have their masses in the ratio of 1 : 7200 and charges in the ratio of 1 : 2. If they start moving from rest through the same electrical potential difference then the ratio of their velocities will be ______.
Given : If particle has charge x coulombs and potential difference y volts . Then gain in K.E. = xy joules.
Using similar analysis,
(mass)electron(mass) alpha particle=17200
(charge)electron(charge) alpha particle=12
We need to find (velocity)electron(velocity) \alpha particle
Since initially there at rest, initial K.E. = 0;
They move through same potential difference. Let potential difference be y volts.
So, gain in K.E = Final K.E – Initial K.E
= Final K.E – 0
So, gain in K.E = charge×potentialdifference
Ratio of gain in K.E of electron and α particle = Ratio of final K.E of electron and α particle
12mv2e×y12mv2α×y
=12×7200=3600
vevα=√3600=60