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

Explanation

Let `m_(1) m_(2)` be the masses of products and `vec(upsilon_(1)),vec (upsilon_(1))` be thir respective velocities Therefore total linear momentum after disintegration ` = m_(1) vec(upsilon_(1)) + m_(2) vec (upsilon_(2)) ` 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_(1) vec(upsilon_(1)) + m_(2) vec(upsilon_(2)) = 0 or vec(upsilon_(2)) = (-m_(1) vec(upsilon_(1)))/m_(2) `
Negative sign shown that `vec(v_(1)) and vec(v_(2)` are in opposite directions.