A nucleus with mass number 220, initially at rest, emits an α − particle. If the Q - value of the reaction…

A nucleus with mass number 220, initially at rest, emits an α− particle. If the Q- value of the reaction is 5.5 MeV, the kinetic energy of the α- particle is
  1. 4.4 MeV
  2. 5.4 MeV
  3. 5.6 MeV
  4. 6.5 MeV

Solution

Let K1 & K2 and P1 & P2 are the K.E. and momentum of the α- particle and remaining nucleus, then

K1+K2=5.5 MeV ......(i)

From the conservation of linear momentum

P1=P2⇒2K1×4m ⇒K1=54K2 ......(ii)

From (i) and (ii)

K1=5.5×5455=5.4 MeV

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