First slide

Radio activity

Question

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

Moderate

A

4.4MeV
B

5.4MeV
C

2.75MeV
D

6.5MeV

Solution

Let $K_{1} & K_{2} and P_{1} & P_{2}$ are the K.E and momentum of the $α$ -particle and remaining nucleus, then $K_{1} + K_{2} = 5.5 MeV$ --- (i)
From conservation of linear momentum $P_{1} = P_{2}$
$\Rightarrow \sqrt{2 K_{1} \times 4 m} = \sqrt{2 K_{2} \times 216 m} \Rightarrow K_{1} = 54 K_{2}$ --- (ii)
From (i) and (ii) $K_{1} = \frac{5.5 \times 54}{55} = 5.4 MeV$

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