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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 :

Text Solution

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Using conservation of momentum
`mv_(0)=mv_(2)-mv_(1)`

`1/2mv_(1)^(2)=0.36xx1/2mv_(0)^(2)`
`impliesv_(1)=0.6v_(0)`
The collision is elastic. So,
`1/2 MV_(2)^(2)=0.64xx1/2mv_(0)^(2)` [ `:.` M= mass of nucleus]
`impliesV_(2)=sqrt(m/M)xx0.8V_(0)`
`mV_(0)=sqrt(mM)xx0.8V_(0)-mxx0.6V_(0)`
`implies1.6m=0.8sqrt(mM)`
`implies4m^(2)=mM`
`:.M=4m`
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