Sol. We assume that a perfectly inelastic collision

occurs between incident particle and hydrogen atom. From conservation of momentum, we can write

mv 0 = (m + m H )u

Initial kinetic energy W 0 =

Final kinetic energy W = (m + m H )u 2 =

The decrease in kinetic energy,

W 0 – W = –

= W 0

This decrease in kinetic energy must be equal to

ionization energy.

W i = (W 0 )

which shows that the greater the mass of the incident

particle, the smaller the fraction of the initial kinetic

energy that can be used for ionization. When an

electron in used, m e << m H , i.e., W i W 0 , hence, the

initial kinetic energy of the electron is almost completely used for ionization. When a hydrogen atom

is used, the initial kinetic energy must be double that of the electron. For a helium atom,

W 0 – W i = = W 0

i.e., the energy must be five times that of the electron.

Note that in a gas-discharge plasma, ionization is

carried out almost by electrons, while ionization by the ions plays an insignificant role.