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A uranium-238 nucleus initially at rest undergoes alpha decay and the emitted alpha particle moves with speed v. What is the recoil speed of the daughter nucleus?
- 4v/238
- 4v/234
- 4v/234
- 4v/238
Correct answer: 4v/234
Solution
In alpha decay, momentum is conserved. The initial momentum is zero, so the momentum of the emitted alpha particle must equal the momentum of the recoiling daughter nucleus. Given the mass of the alpha particle is 4 and the mass of the daughter nucleus is 234, the recoil speed can be calculated as the speed of the alpha particle divided by the mass ratio, resulting in 4v/234.
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