Question
A nucleus is at rest in the laboratory frame of reference. Show that if it disintegrates into two smaller nuclei the products must move in opposite directions.
✓
Answer
Let, Mass of parent nucleus $=\mathrm{m}$ (At rest) Mass of two daughter nuclei $=\mathrm{m}_1$, and $\mathrm{m}_2$ Initial momentum of the system (parent nucleus) $=0$ Let, Velocity of first daughter nucleus having mass $m_1=v_1$ Velocity of second daughter nucleus having mass $m_2=v_2$ Total linear momentum of the system after disintegration $=\left(m_1 v_1+m_2 v_2\right)$ According to the law of conservation of momentum: Total initial momentum $=$ Total final momentum $0=\left(m_1 \mathrm{v}_1+m_2 \mathrm{v}_2\right) \mathbf{v}_1=\frac{-\mathrm{m}_2 \mathbf{v}_2}{\mathrm{~m}_1}$ Here, the negative sign indicates that the fragments of the parent nucleus move in directions opposite to each other.
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