A hydrogen atom `(mass = 1.66 xx 10^(-27)` kg "ionzation potential" = 13.6eV)`, moving width a velocity `6.24 xx 10^(4) m s^(-1)` makes a completely inelastic head-on collision with another stationary hydrogen atom. Both atoms are in the ground state before collision . Up to what state either one atom may be excited?

Answer

2

Explanation

Using `COM: mu = 2 mv`
`v = (u)/(2) , Delta E = (1)/(2) mu^(2) - 2 xx (1)/(2) m ((u)/(2))^(2)`
`implies Delta E = (1)/(4) mu^(2) = (1)/(4) xx 1.66 xx 10^(-27) xx (6.24 xx 10^(4)) ^(2)`
`= 13.6 ((1)/(l^(2)) - (1)/(n^(2)))`
`= (1.66 xx 10^(-27) xx 6.24 xx 10^(4)) ^(2)/(4 xx 1.6 xx 10^(-19)) implies n = 2`