Question

g What is the minimum speed needed by a ground-state hydrogen atom for its kinetic energy to be enough to ionize the atom in a collision

Answer 1

Solution ⟹

Let u be velocity of hydrogen atom before collision and V the ve locity of two atoms moving together after collision By principal of conservation of momentum , we have

`Mu + M * 0 = 2VM`

`V = (u)/(2) \\`

The loss in kinetic energy Δϵ due to collision is

`Δϵ= (1)/(2)Mu {}^(2) − (1)/(2) (2M)V {}^(2) \\`

`As, V = (u)/(2) \: we \: have \: Δϵ= (1)/(2)Mu {}^(2) − (1)/(2) (2M)( (u)/(2)) {}^(2) \\`

`= (1)/(2) Mu {}^(2) - (1)/(4)Mu { }^(2) = (1)/(4) Mu {}^(2) \\`

Rest answer is in the pic