Question
a. Calculate the energy released if ${ }^{238} \mathrm{U}$ emits an $\alpha$-particle.
b. Calculate the energy to be supplied to ${ }^{238} \mathrm{U}$ it two protons and two neutrons are to be emitted one by one. The atomic masses of ${ }^{238} \mathrm{U},{ }^{234} \mathrm{Th}$ and ${ }^4 \mathrm{He}$ are $238.0508 \mathrm{u}, 234.04363 \mathrm{u}$ and $4.00260 u$ respectively.

Answer

a. $\mathrm{U}^{238}{ }_2 \mathrm{He}^4+\mathrm{Th}^{234}$
$E= {\left.\left[M u-\left(N_{H C}+M_{T h}\right)\right] u=238.0508-(234.04363+4.00260)\right] u=4.25487 \mathrm{Mev}=4.255 \mathrm{Mev} . }$
$\quad \text { b. } E=U^{238}-\left[T h^{234}+2 n_0^{\prime}+2 p_1^{\prime}\right]$
=$\{238.0508-[234.64363+2(1.008665)+2(1.007276)]\} u$
=$0.024712 u=23.0068=23.007 \mathrm{MeV} .$

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