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.

Answer 1

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.

$$\begin{gathered} \Rightarrow 4\times 1.4\times {10}^7=234\times v_2 \\ {v}_2=\frac{4\times 1.4\times {10}^7}{234}=2.4\times {10}^5\mathrm{m}/\mathrm{s} \end{gathered}$$

Therefore, the speed of the residual nucleus is $2.4\times {10}^5\mathrm{m}/\mathrm{s}$.