Two nuclei fuse in a stellar core according to the reaction: Atomic masses (in u): ,

PHYSICS · Multi-part · A Level · Physics · Nuclear physics · Nuclear physics

Problem

Two

^{3}_{2}\mathrm{He}

nuclei fuse in a stellar core according to the reaction:

^{3}_{2}\mathrm{He}+{}^{3}_{2}\mathrm{He}\;\longrightarrow\;{}^{4}_{2}\mathrm{He}+2\,{}^{1}_{1}\mathrm{H}

Atomic masses (in u):

^{3}_{2}\mathrm{He}=3.016029

^{4}_{2}\mathrm{He}=4.002603

, proton

=1.007825

. Take

1\,\text{u}=931.5\,\text{MeV}/c^2

and

1\,\text{MeV}=1.6\times10^{-13}\,\text{J}

. Solve the following. (i) Find the Q-value of the fusion reaction in MeV. (ii) Convert the Q-value to joules. (iii) If the stellar core produces

5.0\times10^{38}

such fusion events each second, calculate the total power output in watts due to this reaction alone.