E.5 Fusion and stars

The question asks about hydrostatic equilibrium, which is a key concept describing the stable state of a star during its main sequence lifetime.

Hydrostatic equilibrium occurs when the two competing forces acting on a star are exactly balanced: gravity pulling inward and radiation pressure (from nuclear fusion in the core) pushing outward.

The option stating that inward gravitational force is exactly balanced by outward radiation pressure from nuclear fusion precisely captures this definition. No other option describes a force balance.

We need the option that correctly defines hydrostatic equilibrium in a star.

'The star's luminosity is equal to its surface temperature in appropriate units' is incorrect. Luminosity and surface temperature are related but are never simply 'equal' — this is not a definition of equilibrium.

'The rate of hydrogen fusion equals the rate of helium fusion' is incorrect. In most of a star's life, only hydrogen fusion occurs in the core; helium fusion happens at a later stage. This is not what hydrostatic equilibrium means.

'The star's core temperature remains constant throughout its lifetime' is incorrect. Core temperature does change over the star's life; hydrostatic equilibrium is about force balance, not temperature constancy.

The remaining option — inward gravitational force balanced by outward radiation pressure from nuclear fusion — is the correct definition of hydrostatic equilibrium.

This question tests understanding of mass defect and Einstein's mass-energy equivalence ($E=m{c}^2$) as applied to nuclear fusion.

In nuclear fusion, the product nucleus (helium-4) has less mass than the combined mass of the reactants (four protons). This difference in mass is called the mass defect, $\Delta m$.

The mass defect is converted into energy according to $E=m{c}^2$. Since $c^2=9\times 10^{16}{\text{m}}^2{\text{s}}^{-2}$, even a tiny mass defect produces a large amount of energy.

The correct statement is that the helium nucleus has less mass than the four protons, and this mass defect is converted to energy via $E=m{c}^2$.

We need to identify the correct explanation for why energy is released during hydrogen fusion.

'The helium nucleus has more mass than the four protons combined' is factually wrong. The helium nucleus has less mass — if it had more mass, energy would need to be absorbed, not released.

'The strong nuclear force releases stored potential energy when protons bond' is a misleading description. While the strong force is involved in binding, the energy released in fusion is specifically due to the mass defect converted via $E=m{c}^2$, not simply 'stored potential energy' being released.

'Energy is released because Coulomb repulsion does work on the helium nucleus' is incorrect. Coulomb repulsion actually opposes fusion; it does not release energy in this context.

The correct answer is that the helium nucleus has less mass than the four protons, and this mass defect is converted to energy via $E=m{c}^2$.