A) 4.4 MeV
B) 5.4 MeV
C) 5.6 MeV
D) 6.5 MeV
Correct Answer: B
Solution :
[b]: From the law of conservation of linear momentum, we get\[{{p}_{1}}={{p}_{2}}\] But \[p=\sqrt{2mK}\]where K = kinetic energy \[\therefore \]\[\sqrt{2(216m){{K}_{1}}}=\sqrt{2(4m){{K}_{2}}}\] where \[{{K}_{1}}\]is for nucleus and \[{{K}_{2}}\]is for \[\alpha \] particle or \[216{{K}_{1}}=4{{K}_{2}}\]or \[{{K}_{2}}=54{{K}_{1}}\] .... (i) Given : \[{{K}_{1}}+{{K}_{2}}=5.5MeV\] .... (ii) From equations (i) and (ii), we get \[{{K}_{1}}+54{{K}_{1}}=5.5MeV\] or\[55{{K}_{1}}=5.5MeV\] or\[{{K}_{1}}=\frac{5.5}{55}MeV\] or\[{{K}_{1}}=\frac{1}{10}MeV\] \[\because \]\[{{K}_{2}}=54{{K}_{1}}\]or\[{{K}_{2}}=\frac{54}{10}MeV\] or\[{{K}_{2}}=5.4MeV\] \[\therefore \]Kinetic energy of a particle = 5.4 MeV
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