Question

# A radioactive nucleus of mass number A, initially at rest, emits an α - particle with a speed v. What will be the recoil speed of the daughter nucleus?

A
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B
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C
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D
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Solution

## The correct option is C The total number of nucleons (i.e. protons + neutrons) in a nucleus is called its mass number. An α-particle is a helium nucleus having 2 protons and 2 neutrons. So the mass number of an α - particle = 4. When a nucleus of mass number A emits an α - particle, the mass number of the daughter nucleus reduces to (A – 4). If V is the recoil speed of the daughter nucleus, we have, from the law of conservation of momentum, (A – 4)V-4v = 0 or V=4vA−4 Hence the correct choice is (c)

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