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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.
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Solution
Let the masses of the two resulting nuclei be represented as m1 and m2, and their velocities as v1 and v2 respectively. Thus, the total linear momentum after disintegration = m1v1 +m2 v2. Before disintegration, the nucleus is at rest. Therefore, its linear momentum before disintegration is zero.
According to the principle of conservation of linear momentum,
`m_1vecv_1 + m_2vecv_2 = 0 or vecv_2 = - (m_1vecv_1)/m_2`
The negative sign indicates that v1 and v2 point in opposite directions.
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