Suppose our apparatus will only allow us to distinguish the first order bright fringe from the central bright spot if they are s
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Assume that the small-massed particle is and the heavier mass particle is
.
Now, by momentum conservation and energy conservation:
Now, there are 2 solutions but, one of them is useless to this question's main point so I excluded that point. Ask me in the comments if you want the excluded solution too.
So now, we see that and
. So therefore, the smaller mass recoils out.
Hope this helps you!
Bye!