At the end of its life, a star with a mass of two times the...

At the end of its life, a star with a mass of two times the Sun’s mass is expected to collapse, combining its protons and electrons to form a neutron star. Such a star could be thought of as a gigantic atomic nucleus. If a star of mass $2 \times 1.99 \times$ $10^{30} \mathrm{kg}$ collapsed into neutrons $\left(m_{n}=1.67 \times 10^{-27} \mathrm{kg}\right)$ what would its radius be? Assume $r=r_{0} A^{1 / 3}$.

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Key Concepts

Neutron Stars

Neutron stars are the dense remnants of massive stars that have undergone gravitational collapse after exhausting their nuclear fuel. They are composed almost entirely of neutrons and are characterized by incredibly high densities, where matter is packed so tightly that a teaspoon of neutron star material would weigh billions of tons on Earth.

Nuclear Radius Scaling Law

The nuclear radius scaling law, expressed as r = r?A^(1/3), relates the radius of a nucleus to its mass number A. This empirical relationship reflects the nearly constant density of nuclear matter and is used to estimate the size of nuclei—including, in extreme cases, stellar objects like neutron stars when they are treated as gigantic nuclei.

Mass Number Calculation

The mass number A in this context is determined by dividing the total mass of the collapsed star by the mass of a single neutron. This calculation provides the effective number of neutrons in the star, which can then be used with the nuclear radius scaling law to estimate the overall radius.

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