Question 18

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:

In nuclear fission: $$M \rightarrow 3 \times \frac{M}{3}$$. Mass defect = $$\Delta M$$.

Energy released: $$E = \Delta M c^2$$.

This energy is shared as kinetic energy among three identical daughter nuclei: $$3 \times \frac{1}{2} \cdot \frac{M}{3} \cdot v^2 = \Delta M c^2$$.

$$\frac{M v^2}{2} = \Delta M c^2$$

$$v^2 = \frac{2\Delta M c^2}{M}$$

$$v = c\sqrt{\frac{2\Delta M}{M}}$$

The answer is Option (3): $$\boxed{c\sqrt{\frac{2\Delta M}{M}}}$$.

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