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  4. A nucleus with mass number 184 initially at rest emits an α-particle. If the Q value of the reaction is 5.5 MeV, calculate the kinetic energy of the α- particle.

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Q. A nucleus with mass number $184$ 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.

JEE MainJEE Main 2021Nuclei

Solution:

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$\frac{1}{2}(4 m) v^{2}+\frac{1}{2}(180 m)\left(\frac{4 v}{180}\right)^{2}=5.5\, MeV$
$\Rightarrow \frac{1}{2} 4 m v^{2}\left[1+45\left(\frac{4}{180}\right)^{2}\right]=5.5\, MeV$
$\Rightarrow K . E_{a}=\frac{5.5}{1+45 \cdot\left(\frac{4}{180}\right)^{2}} MeV$
$K \cdot E_{\alpha}=5.38\, MeV$