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,

detailed solution

Correct option is C

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.