Solution
ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2025/ii/paper-2/9e/d/solution
Past exam of the mathematics course of the University of Cambridge 2025 ii Paper 2 9E d Solution by
Codex 0 Created 2026-09-24 Updated 2026-09-25
Increasing makes smaller at every fixed temperature, so freeze-out occurs earlier, at a higher . The equilibrium value is then closer to one. Although some neutrons subsequently decay, the final neutron fraction is larger, andincreases, approaching unity if the surviving neutron and proton abundances become comparable.
Such a universe begins with less hydrogen and more helium. It has less fuel for long-lived hydrogen-burning stars; stellar evolution would tend to proceed through hotter, faster helium-burning stages, reducing typical stellar lifetimes. The shorter stable-energy window, altered heavy-element production, and lower primordial hydrogen abundance would make familiar water-rich, slowly evolving habitats less likely, although a detailed conclusion would require a stellar-evolution model.
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