A proton collides with a stationary deuteron to form a He 3 nucleus. For this reaction to take place, the proton must have a minimum kinetic energy K 0 . If instead, a deuteron collides with a stationary proton to make a He 3 nucleus, then it must have minimum kinetic energy equal to

Step-by-step solution

In case 1: Conservation of linear momentum: mv 0 = 3 mv ⇒ v = v 0 3 Conservation of mechanical energy: 1 2 mv 0 2 = 1 2 3 m v 0 3 2 + U 0 Here U 0 is the minimum energy required for the reaction to happen ⇒ U 0 = K 0 - K 0 3 = 2 K 0 3 In case 2: Conservation of linear momentum: 2 mv 0 ' = 3 mv ' ⇒ v ' = 2 3 v 0 ' Conservation of mechanical energy: 1 2 2 m v 0 ' 2 = 1 2 3 m 2 3 v 0 ' 2 + 2 K 0 3 ⇒ mv 0 ' 2 - 2 3 mv 0 ' 2 = 2 K 0 3 ⇒ 1 3 mv 0 ' 2 = 2 K 0 3 ⇒ 1 2 2 mv 0 ' 2 = 2 K 0