# Problem: Consider a fusion reaction in which a proton fuses with a neutron to form a deuterium nucleus. How much energy is released in this reaction? (The mass of the deuterium nucleus is 2.01355u). Answer in MeV.

###### FREE Expert Solution

The energy released in the reaction:

$\overline{){\mathbf{E}}{\mathbf{=}}{\mathbf{∆}}{\mathbf{m}}{{\mathbf{c}}}^{{\mathbf{2}}}}$

The reaction process is:

${}_{\mathbf{1}}^{\mathbf{1}}\mathbit{H}\mathbf{\left(}\mathbit{p}\mathbit{r}\mathbit{o}\mathbit{t}\mathbit{o}\mathbit{n}\mathbf{\right)}{\mathbf{+}}_{\mathbf{0}}^{\mathbf{1}}\mathbit{n}{\mathbf{\to }}_{\mathbf{1}}^{\mathbf{2}}\mathbit{H}$

The reduced mass is obtained from:

$\begin{array}{rcl}\mathbf{∆}\mathbf{m}& \mathbf{=}& {\mathbf{m}}_{\mathbf{p}}\mathbf{+}{\mathbf{m}}_{\mathbf{n}}\mathbf{-}{\mathbf{m}}_{{}_{\mathbf{1}}^{\mathbf{2}}\mathbf{H}}\\ & \mathbf{=}& \mathbf{1}\mathbf{.}\mathbf{0072766}\mathbf{+}\mathbf{1}\mathbf{.}\mathbf{0086654}\mathbf{-}\mathbf{2}\mathbf{.}\mathbf{01355}\end{array}$

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###### Problem Details

Consider a fusion reaction in which a proton fuses with a neutron to form a deuterium nucleus. How much energy is released in this reaction? (The mass of the deuterium nucleus is 2.01355u). Answer in MeV.