## Related questions with answers

Reactions in which kinetic energy is lost $(\Delta K<0)$ are called endothermic and cannot occur below a minimum (threshold) initial energy. (Reactions in which kinetic energy is released are called exothermic.) Which of the following reactions are endothermic, and what are their threshold kinetic energies? (a) $\mathrm{n}+{ }^{208} \mathrm{~Pb} \rightarrow \mathrm{p}+{ }^{208} \mathrm{Tl}$ (b) $\mathrm{n}+{ }^{207} \mathrm{~Pb} \rightarrow \alpha+{ }^{204} \mathrm{Hg}$ (c) $\mathrm{n}+{ }^{187} \mathrm{Os} \rightarrow \mathrm{p}+{ }^{187} \mathrm{Re}$ (d) $\mathrm{n}+{ }^{197} \mathrm{Au} \rightarrow{ }^2 \mathrm{H}+{ }^{196} \mathrm{Pt}$

Solution

VerifiedThe change in kinetic energy can be computed as the change in rest mass. That is,

$\Delta K=K_f-K_i=(M_i-M_f)c^2$

If $\Delta K>0$, kinetic energy is released, and the process is called exothermic. If $\Delta K<0$, the process is called endothermic and requires the energy $|\Delta K|$ in order to proceed.

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