Two hydrogen atom collide Collide head on and end up with zero kinetic energy. Each atom then emit a photon of wavelength `121.6 nm`. Which transition leads to the wavelength? How fast were the hydrogen atoms travelling before collision?

Answer

`n_(1)=1;n_(2)=2;4.43xx10^(4)m" "sec^(-1)`.

Explanation

Wavelength is in UV region, thus `n_(1)` will be 1.
`(1)/(121.6xx10^(-9))=1.097xx10^(7)xx1^(2)xx((1)/(1^(2))-(1)/(n_(2)^(2)))`
`n_(2)=2`
`(1)/(2)mv^(2)=(hc)/(lamda)`
`(1)/(2)xx1.67xx10^(-27)xxv^(2)=(6.626xx10^(-34)xx3xx10^(8))/(121.6xx10^(-9))`
`v=4.43xx10^(4)m" "sec^(-1)`.