A nucleus is at rest in the laboratory frame of reference. Show that if it disintegrates into two smaller nuclei the products must be emitted in opposite directions.

Explanation

Let `m_1`, `m_2` be the masses of products and `v_1`, `v_2` be their respective velocities. Therefore, total linear momentum after disintegration = ` m_(1)v_(1) + m_(2)v_(2)` . Before disintegration , the nucleus is at rest. Therefore, its linear momentum before disintegration is zero . According to the people of conservation of linear momentum,
`m_1``vec (v_1)` + `m_2``vec v_2` = 0 or `vec v_2` = `- m_1``vec v_1` / `m_2`
Negative sign shows that `v_1` and `v_2` are in opposite directions.