In the core of a star

PHYSICS · Multi-part · AP · Physics 2: Algebra-based · Modern Physics · Modern Physics

Problem

In the core of a star, four protons ultimately combine to form one helium-4 nucleus through a sequence of steps often summarised as

4\,{}^1_1\mathrm H \;\longrightarrow\; {}^4_2\mathrm{He}+2e^{+}+2\nu+\text{energy}.

Atomic masses are given below:

^1_1\mathrm H = 1.007825\,\text{u}

^4_2\mathrm{He} = 4.002603\,\text{u}

e^{+} = 0.0005486\,\text{u}

. Use

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

. (a) Compute the mass defect for the net reaction shown. (b) Hence find the energy released per helium-4 nucleus produced, in MeV. (c) Calculate the energy released when 1 g of hydrogen is completely converted into helium-4 by this process. (d) The Sun converts roughly

6.0\times10^8\,\text{kg}

of hydrogen into helium every second. Estimate its power output (in watts) associated with this conversion alone.

Related theory

Mass-Energy Equivalence
Nuclear Fusion
Nuclear Reactions
Nuclear physics
Atomic Structure
Nuclear fusion (stars as energy sources)
Nuclei

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