Two particles A and B of de-broglie wavelength `lambda_(1) and lambda_(2)` combine to from a particle C. The process conserves momentum. Find the de-Broglie wavelength of the particle C. (The motion is one dimensional).

Explanation

Momentum of particle in terms of de Broglie wavelength can be written as `p = h / lamda`
There are two possible cases in one - dimensional motion.
(i) Both particles move in same direction : `p=p_1+p_2`
`impliesh/lamda=h/lamda_1+h/lamda_2implieslamda=(lamda_1lamda_2)/(lamda_1lamda_2)`
(ii) Both particles move in opposite directions :
`p=|p_1-p_2|`
`impliesh/2=|h/(lamda1)-h/lamda_2|implieslamda-(lamda_1lamda_2)/(|lamda_2-lamda_2|)`