Question

# A uranium-238 nucleus, initially at rest, emits an alpha particle with a speed of 1.4 × 107 m/s. Calculate the recoil speed of the residual nucleus thorium-234. Assume that the mass of a nucleus is proportional to the mass number.

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Solution

## According to the question, uranium 238 nucleus emits an alpha-particle with a speed of 1.4 × 107 m/s. Let the speed of the residual nucleus thorium 234 be v2. By the law of conservation of linear momentum, we have: ${m}_{1}{v}_{1}={m}_{2}{v}_{2}$ Here, m1 and v1 are the mass and velocity of the alpha-particle repectively, and m2 is the mass of the residual nucleus. $⇒4×1.4×{10}^{7}=234×{v}_{2}\phantom{\rule{0ex}{0ex}}{v}_{2}=\frac{4×1.4×{10}^{7}}{234}=2.4×{10}^{5}\mathrm{m}/\mathrm{s}$ Therefore, the speed of the residual nucleus is $2.4×{10}^{5}\mathrm{m}/\mathrm{s}$.

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