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Question
A uranium-238 nucleus, initially at rest, emits an alpha particle with a speed of 1.4 × 107m/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.
\[\Rightarrow 4 \times 1 . 4 \times {10}^7 = 234 \times v_2 \]
\[ v_2 = \frac{4 \times 1 . 4 \times {10}^7}{234} = 2 . 4 \times {10}^5 \text{ m/s }\]
Therefore, the speed of the residual nucleus is
\[2 . 4 \times {10}^5 \text{ m/s}\]
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