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Question

A nucleus of mass number A originally at rest emits α particle with speed v. What will be recoil speed of the daughter nucleus?

A
vA4
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B
vA+4
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C
4vA4
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D
4vA+4
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Solution

The correct option is B 4vA4
When a nucleus emits an α particle its mass number decreases by 4, hence mass of an α particle is 4. The mass of daughter nucleus is (A4).
In the emission of an α particle the momentum remains conserved if v is the recoil velocity of daughter nucleus then,
m1u1+m2u2=(m1m2)v
A(0)+4v=(A4)v
v=4vA4

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