Question 176: Atoms & Nuclei

Question

The explosive in a Hydrogen bomb is a mixture of $${ }_1 \mathrm{H}^2,{ }_1 \mathrm{H}^3$$ and $${ }_3 \mathrm{Li}^6$$ in some condensed form. The chain reaction is given by
$$\begin{aligned}
& { }_3 \mathrm{Li}^6+{ }_0 \mathrm{n}^1 ightarrow{ }_2 \mathrm{He}^4+{ }_1 \mathrm{H}^3 \
& { }_1 \mathrm{H}^2+{ }_1 \mathrm{H}^3 ightarrow{ }_2 \mathrm{He}^4+{ }_0 \mathrm{n}^1
\end{aligned}$$
During the explosion the energy released is approximately
[Given ; $$\mathrm{M}(\mathrm{Li})=6.01690 \mathrm{~amu}, \mathrm{M}\left({ }_1 \mathrm{H}^2ight)=2.01471 \mathrm{~amu}, \mathrm{M}\left({ }_2 \mathrm{He}^4ight)=4.00388$$ $$\mathrm{amu}$$, and $$1 \mathrm{~amu}=931.5 \mathrm{~MeV}]$$

Accepted Answer

$$\begin{aligned}
& { }_3 \mathrm{Li}^6+{ }_0 \mathrm{n}^1 ightarrow{ }_2 \mathrm{He}^4+{ }_1 \mathrm{H}^3 \
& { }_1 \mathrm{H}^2+{ }_1 \mathrm{H}^3 ightarrow{ }_2 \mathrm{He}^4+{ }_0 \mathrm{n}^1 \
& \hline{ }_3 \mathrm{Li}^6+{ }_1 \mathrm{H}^2 ightarrow 2\left({ }_2 \mathrm{He}^4ight) \
& \hline
\end{aligned}$$
Energy released in process
$$\begin{aligned}
& \mathrm{Q}=\Delta \mathrm{mc}^2 \
& \mathrm{Q}=\left[\mathrm{M}(\mathrm{Li})+\mathrm{M}\left(\mathrm{H}^2ight)-2 	imes \mathrm{M}\left({ }_2 \mathrm{He}^4ight)ight] 	imes 931.5 \mathrm{~MeV} \
& \mathrm{Q}=[6.01690+2.01471-2 	imes 4.00388] 	imes 931.5 \mathrm{~MeV} \
& \mathrm{Q}=22.216 \mathrm{~MeV} \
& \mathrm{Q}=22.22 \mathrm{~MeV}
\end{aligned}$$

Answer

22.22 MeV

Answer

28.12 MeV

Answer

16.48 MeV

Answer

12.64 MeV

Atoms & Nuclei

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