A hydrogen atom travelling at a speed v collides with a stationary hydrogen atom. Determine the minimum value of v such that one of the atoms could become ionized. The mass of a hydrogen atom is 1.67 imes 10⁻²⁷ kg .

Step-by-step solution

Let the mass of the hydrogen atom be m and its initial speed be v . For the maximum loss of kinetic energy, the collision must be perfectly inelastic. By conservation of linear momentum, the final common velocity v' of the two atoms is given by: mv = (m + m)v' v' = v 2 The maximum loss in kinetic energy K is: K = 1 2 mv^2 - 1 2 (2m) ( v 2 )^2 = 1 4 mv^2 For one of the hydrogen atoms to be ionized, this loss in kinetic energy must be at least equal to the ionization energy of a hydrogen atom, which is 13.6 eV . 1 4