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A nucleus with mass number 220 initially...

A nucleus with mass number `220` initially at rest emits an `alpha`-particle. If the Q-value of the reaction is `5.5 MeV`, calculate the kinetic energy of the `alpha`-particle.
(a) 4.4 MeV (b) 5.4 MeV (c) 5.6 MeV (d) 6.5 MeV

A

4.4 MeV

B

5.4 MeV

C

5.6 MeV

D

6.5 MeV

Text Solution

Verified by Experts

The correct Answer is:
B
(b)
`Q` - value of the reaction is `5 .5 eV`
i.e., `k_1 +k_2 = 5.5 MeV`…(i)
By conservation of linear momentum
`p_1 = p_2 rArr sqrt(2(216) k_1)`
=`sqrt(2(4)k_2)`
`rArr k_2 = 54 k_1` …(ii)
On solving equation (i) and (ii) we get `k_2 = 5.4 MeV`.
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