A hydrogen atom moving at a speed v absorbs a photon of wavelength 122 nm and stops. The value of v is (mass of hydrogen atom `=1.67xx10^(-27)` kg)

Explanation

(a)
By conservation of momentum
`mv - (h)/(lambda) =0`
`v=(h)/(m lambda) = (6.6xx10^(-34))/(1.67xx10^(-27)xx122xx10^(-9))`
`=3.24 m//sec`
(b) `U=(1)/(4pi in_(0)) (q_(1)q_(2))/(r) =(hc)/(lambda)`
`U =(1)/(4pi in_(0)).(q_(1)q_(2))/(r), (q_(1))_(min) = (q_(2))_(min) =e`
`U_(min) =(1)/(4pi in_(0)) (e.e)/(r) = (9xx10^(9)xx(1.6xx10^(-19))^(2))/(1) J`
`=(9xx10^(9)xx(1.6xx10^(-19))^(2))/(1.6xx10^(-19))eV =14.4xx10^(-10) eV`
`lambda(nm) =(1242)/(U_(min)(eV))nm =(1242)/(14.4xx10^(-10))nm`
`=86.25xx10^(10)nm =862.5m`
`(q_(1))_(min) =(q_(2))_(min) =2e`
`lambda' =(862.5)/(4) =215.6 m`