The fusion reaction $2 \mathrm{H}+3 \mathrm{H} \rightarrow 4 \mathrm{He}+\mathrm{n}$ releases $17.6 \mathrm{MeV}$ of energy. The mass of $2 \mathrm{H}$ is $2.01410 \mathrm{u}$, the mass of $4 \mathrm{He}$ is $4.00260 \mathrm{u}$, and the mass of the neutron is $1.00866 \mathrm{u}$. What is the mass of $3 \mathrm{H}$ ?

Question

Quizplus · Accepted Answer

The mass of $3 \mathrm{H}$ can be found by applying the principle of mass-energy equivalence to the given fusion reaction. The total mass before the reaction is the sum of the masses of $2 \mathrm{H}$ and $3 \mathrm{H}$, and the total mass after the reaction is the sum of the masses of $4 \mathrm{He}$ and the neutron. The difference in mass corresponds to the energy released in the reaction, which is $17.6 \mathrm{MeV}$. Using the given masses for $2 \mathrm{H}$, $4 \mathrm{He}$, and the neutron, and converting the energy released into mass units (using $1 \mathrm{MeV} = 1.783 \times 10^{-30} \mathrm{kg}$ and $1 \mathrm{u} = 1.660539 \times 10^{-27} \mathrm{kg}$), we can solve for the mass of $3 \mathrm{H}$. The calculation confirms that option D is correct.

The Fusion Reaction 2H+3H→4He+n2 \mathrm{H}+3 \mathrm{H} \rightarrow 4 \mathrm{He}+\mathrm{n}2H+3H→4He+n Releases 17.6MeV17.6 \mathrm{MeV}17.6MeV

The Fusion Reaction $2 \mathrm{H}+3 \mathrm{H} \rightarrow 4 \mathrm{He}+\mathrm{n}$ Releases $17.6 \mathrm{MeV}$