In the core of a star

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

Problem

In the core of a star, four protons ultimately combine to form a helium-4 nucleus according to the net reaction 4 11H→24He+2 e++2 νe4\,^{1}_{1}\text H \rightarrow ^{4}_{2}\text{He} + 2\,e^{+} + 2\,\nu_e (The rest‐mass of the neutrino may be taken as zero.) Atomic masses: 11H=1.007825 u^{1}_{1}\text H = 1.007825\,\text u, 24He=4.002603 u^{4}_{2}\text{He} = 4.002603\,\text u, e+=0.0005486 ue^{+} = 0.0005486\,\text u. Constants: 1 u=931.5 MeV/c21\,\text u = 931.5\,\text{MeV}/c^2, NA=6.02×1023 mol−1N_A = 6.02\times10^{23}\,\text{mol}^{-1}. (i) Show that the total mass of the products is less than that of the reactants and hence compute the Q-value of the reaction in MeV. (ii) Calculate the energy released when 1.00 mol1.00\,\text{mol} of hydrogen nuclei undergo this conversion. (iii) Comment, with a quantitative justification, on the role of such reactions in sustaining the luminosity of ordinary stars like the Sun.

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