A nucleus of mass M + Δm is at rest and decays into two daughter nuclei of equal mass M/2 each. Speed of light is c.

The speed of daughter nuclei is

$fraction numerator increment straight m over denominator straight M plus increment straight m end fraction$
$square root of fraction numerator 2 increment straight m over denominator straight M end fraction end root$
$straight c square root of fraction numerator increment straight m over denominator straight M end fraction end root$
$straight c space square root of fraction numerator increment straight m over denominator straight M space plus space increment straight m end fraction end root$

Solution

square root of fraction numerator 2 increment straight m over denominator straight M end fraction end root

Conserving the momentum
$0 space equals space space straight M over 2 straight V subscript 1 space minus space straight M over 2 space straight V subscript 2 space left parenthesis therefore space initial space Velocity space equals space 0 right parenthesis rightwards double arrow space straight v subscript 1 space equals space straight v subscript 2 space..... space left parenthesis straight i right parenthesis$
Now, from energy conservation and mass -energy equivalence

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