The minimum kinetic energy required for ionization of a hydrogen atom is E1 in case electron is collided with hydrogen atom. It is E2 if the hydrogen ion is collided and E3 when helium ion is collided. Then,

Assuming that ionization occurs as a result of a completely inelastic collision, we can writemv−0=m+mHuwhere m is the mass of incident particle, mH the mass of hydrogen atom, v0 the initial velocity of incident particle, and u the final common velocity of the particle after collision. Prior to collision, the KE of the incident particle wasE0=mv022The total kinetic energy after collisionE=m+mHu22=m2v022m+mHThe decrease in kinetic energy must be equal to ion ionization energy. Therefore,E1=E0−E=mHm+mHE0 i.e.,  E1E0=11+mmHi.e., the greater the mass m, the smaller the fraction of initial kinetic energy that be used for ionization.