A hydrogen atom moving at speed `upsilon` collides with another hydrogen atom kept at rest .Find the minimum value of u for which one of the atoms may get ionized the mass of a hydrogen atom `= 1.67 xx 10^(-27)kg`

Answer

A, B, D

Explanation

The hydrogen atoms after collision move with speeds `v_1 and v_2`
`mv=mv_1 + mv_2` …(1)
`1/2mv^2 = 1/2mv_1^2 +1/2mv_2^2 +DeltaE` …(2)
From (1)
`v^2 = (v_1+v_2)^2`
`=v_1^2 +v_2^2 +2v_1v_2`
From (2)
`v^2 = v_1^2 + 2DeltaE//M`...(3)
[ `:'2v_1v_2 = (2 Delta E)/M`]
`(v_1 -v_2)^2 = (v_1 + v_2)^2-4v_1v_2`
implies `(v_1 -v_2) = sqrt((v_1 +v_2)^2 -4 Delta E//M)`
for minimum value of 'v'
`v^2 = (4 Delta E)/m`
`=(4xx13.6 xx 1.6 xx 10^-19)/(1.67 xx 10^-27)`
`v=sqrt ((4 xx 13.6 xx 1.6 xx 10^8)/(1.67 xx 10^-27))`
`=10^4sqrt((4 xx 13.6 xx 1.6)/(1.67))`
`=7.2 xx 10^4 m/s`