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An alpha-particle of mass m suffers 1-di...

An alpha-particle of mass m suffers `1`-dimentinal eleastic collision with a nucleus at rest of unknown mass. It is scattered directly backwards losing `64%` of its initial kinetic energy. The mass of the nucleus is :

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The correct Answer is:
4
Let kinetic energy = K
From law of conservation of momentum
`sqrt(2mK) = -sqrt(2m xx 0.36 K) + sqrt(2M xx 0.64 K)`
`1 = =sqrt(0.36) + sqrt((M)/(m) xx 0.64), 1+ 0.6 = 1.6 = sqrt((M)/(m)) xx 0.8`
`sqrt((M)/(m)) = 2 rArr M = 4m`
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