\( 2 \quad 5 \) points
An atom of uranium-235 (of atomic mass equal to 235 atomic mass units or amu) is at rest when it undergoes nuclear fission, decaying into thorium-231 (m = 231 \( \mathrm{amu} \) ) and an alpha particle (a helium nucleus, \( \mathrm{m}=4 \mathrm{amu} \) ). The alpha particle has a speed of \( 4.0^{*} 10^{3} \mathrm{~m} / \mathrm{s} \) to the right. We assume that classical mechanics can characterize this system, and that relativistic effects can be ignored (weird things happen to small masses travelling quickly that are not described by the classical mechanics we now study). Determine the recoil speed in \( \mathrm{m} / \mathrm{s} \) of the thorium nucleus.
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Answer
Substitute values and calculate: \( v_{\text{Th}}= \cfrac{(4)(4.0\times 10^3)}{231} \approx 69.2641 \mathrm{~m} / \mathrm{s} \).
Step 1 ：Since momentum is conserved, we have \( m_{\text{Th}}v_{\text{Th}} = m_{\text{He}}v_{\text{He}} \).
Step 2 ：Solving for the thorium velocity: \( v_{\text{Th}}= \cfrac{m_{\text{He}}v_{\text{He}}}{m_{\text{Th}}} \).
Step 3 ：Substitute values and calculate: \( v_{\text{Th}}= \cfrac{(4)(4.0\times 10^3)}{231} \approx 69.2641 \mathrm{~m} / \mathrm{s} \).
