JEE MAIN - Physics (2024 - 30th January Evening Shift - No. 10)
In a nuclear fission reaction of an isotope of mass $$M$$, three similar daughter nuclei of same mass are formed. The speed of a daughter nuclei in terms of mass defect $$\Delta M$$ will be :
$$c \sqrt{\frac{3 \Delta M}{M}}$$
$$\frac{\Delta M c^2}{3}$$
$$c \sqrt{\frac{2 \Delta M}{M}}$$
$$\sqrt{\frac{2 c \Delta M}{M}}$$
Explanation
$$\begin{aligned}
& \begin{aligned}
& (\mathrm{X}) \rightarrow(\mathrm{Y})+(\mathrm{Z})+(\mathrm{P}) \\
& \begin{array}{llll}
\mathrm{M} & \mathrm{M} / 3 & \mathrm{M} / 3 & \mathrm{M} / 3
\end{array} \\
\end{aligned} \\
& \Delta \mathrm{Mc}^2=\frac{1}{2} \frac{\mathrm{M}}{3} \mathrm{~V}^2+\frac{1}{2} \frac{\mathrm{M}}{3} \mathrm{~V}^2+\frac{1}{2} \frac{\mathrm{M}}{3} \mathrm{~V}^2 \\
& \mathrm{~V}=\mathrm{c} \sqrt{\frac{2 \Delta \mathrm{M}}{\mathrm{M}}}
\end{aligned}$$
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