A) \[4.2\left( 1+\frac{4}{238} \right)MeV\]
B) \[4.2\left( \frac{234}{238} \right)MeV\]
C) \[4.2\left( \frac{238}{234} \right)MeV\]
D) \[4.2\left( 1-\frac{4}{234} \right)MeV\]
Correct Answer: C
Solution :
| Uranium nucleus is initially at rest. Conservation of momentum gives |
| \[0={{p}_{\alpha }}+{{p}_{Th}}\]\[\Rightarrow \]\[{{p}_{Th}}=-{{P}_{\alpha }}\] |
| Also, \[Q={{K}_{a}}+{{K}_{Th}}\] |
| \[\Rightarrow \]\[Q={{K}_{\alpha }}+p_{Th}^{2}/2{{m}_{Th}}\] |
| \[={{K}_{\alpha }}+\frac{p_{\alpha }^{2}}{2{{m}_{Th}}}={{K}_{\alpha }}+\frac{2{{m}_{a}}\cdot {{K}_{\alpha }}}{2{{m}_{Th}}}\] |
| \[={{K}_{\alpha }}\left( 1+\frac{{{m}_{\alpha }}}{{{m}_{Th}}} \right)=4.2\left( 1+\frac{4}{234} \right)\] |
| \[=4.2\left( \frac{238}{234} \right)MeV\] |
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