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Chapter 40: Problem 20

A neutron star is essentially a gigantic nucleus with mass 1.35 times that of the Sun, or mass number of order \(10^{57} .\) It consists of approximately \(99 \%\) neutrons, the rest being protons and an equal number of electrons. Explain the physics that determines these features.

Short Answer

Expert verified
Answer: Neutron stars are remnants of massive stars that have undergone supernova explosions, leading to a high concentration of neutrons. The key properties of a neutron star, such as its mass (about 1.35 times that of the sun), mass number (approximately 10^57), and composition (99% neutrons, with the remaining 1% consisting of protons and electrons), are determined by the interplay between gravity and degeneracy pressure. Forces within the star balance each other, with gravity compressing the star and degeneracy pressure, a quantum mechanical effect, opposing this compression. Neutron stars also contain a small number of protons and electrons due to beta-minus decay, which helps in maintaining the overall balance of forces within the star.

Step by step solution

01

Discuss the Origin of Neutron Stars

Neutron stars are the remnants of massive stars that have gone through a supernova explosion. Due to the collapse of the massive star's core, protons and electrons merge, resulting in a high, almost pure, concentration of neutrons. This is the main reason why the neutron star is approximately 99% neutrons.
02

Describe the Properties of Neutron Stars

Neutron stars are incredibly dense, with mass numbers on the order of \(10^{57}\) and radii of the order of 10 km. This high density leads to the strong presence of forces acting on the neutrons, protons, and electrons within the neutron star, which will define its composition.
03

Gravity and Degeneracy Pressure in Neutron Stars

The two primary forces at play inside neutron stars are gravity and degeneracy pressure. Gravity tends to compress the neutron star even further and inwards due to the star's immense mass. However, as neutrons are fermions, they exert degeneracy pressure (a quantum mechanical effect) which opposes the compressive force of gravity, preventing the neutron star from collapsing further.
04

Explain the Beta-minus Decay and its Relevance to Neutron Stars

For a stable neutron star, gravitational force must be balanced by degeneracy pressure. At extremely high densities, some neutrons can undergo beta-minus decay, turning into a proton and an electron: \[ n \rightarrow p + e^{-} + \bar{\nu}_{e} \] This process is relevant to neutron stars as it increases the number of negatively charged particles (electrons) and positively charged particles (protons), which contribute to the overall balance of forces within the star.
05

Understanding the 99% Neutron Composition

Since neutron stars are formed through the merger of protons and electrons, their composition is dominated by neutrons. However, a small number of protons and electrons are present due to beta-minus decay. The amount of protons and electrons in a neutron star is consistently on the order of 1% of the total particles present, leading to the 99% neutron composition.
06

Concluding Remarks

The key features of a neutron star, such as its mass (~1.35 times that of the sun), mass number (around \(10^{57}\)), and composition (approximately 99% neutrons, with the remaining consisting of protons and electrons), are determined by the processes involved in its formation as well as the interplay between the gravity and degeneracy pressure. The balance of these forces and particle interactions results in the stable, incredibly dense, and neutron-rich structure of neutron stars.

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Most popular questions from this chapter

Billions of years ago, our Solar System was created out of the remnants of exploding stars. Nuclear scientists believe that two isotopes of uranium, \({ }^{235} \mathrm{U}\) and \({ }^{238} \mathrm{U},\) were created in equal amounts at the time of a stellar explosion. However, today \(99.28 \%\) of uranium is in the form of \({ }^{238} \mathrm{U}\) and only \(0.72 \%\) is in the form of \({ }^{235} \mathrm{U}\). Assuming a simplified model in which all of the matter in the Solar System originated in a single exploding star, estimate the approximate time of this explosion.

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\(^{214} \mathrm{Pb}\) has a half-life of \(26.8 \mathrm{~min}\). How many minutes must elapse for \(90.0 \%\) of a given sample of \({ }^{214} \mathrm{~Pb}\) atoms to decay?

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