E.5 核聚變與恆星：練習題

A stable star on the main sequence is in a state of hydrostatic equilibrium. Which two forces are balanced in this state?

When a main sequence star exhausts the hydrogen fuel in its core, what is the most immediate change that occurs to the core's physical state?

A very massive star, with an initial mass significantly greater than eight solar masses, is approaching the end of its life. Its core has already exhausted its hydrogen and helium fuel. Which of the following statements best describes the subsequent nuclear fusion processes and the ultimate fate of the star's core before a supernova explosion?

Which element serves as the primary fuel for the proton-proton chain reaction in the core of a star like the Sun?

The binding energy per nucleon for deuterium \( (_{1}^{2}\text{H}) \) is \( 1.11 \text{ MeV} \) and for helium-4 \( (_{2}^{4}\text{He}) \) is \( 7.07 \text{ MeV} \). What is the total energy released in the fusion reaction \( _{1}^{2}\text{H} + _{1}^{2}\text{H} \rightarrow _{2}^{4}\text{He} \)?

Explain the two fundamental conditions necessary for sustained nuclear fusion within a star's core, and briefly describe why achieving these same conditions on Earth for controlled fusion is a significant challenge.

For a massive main-sequence star, the CNO cycle is the primary mechanism for hydrogen fusion. Explain the role of carbon, nitrogen, and oxygen in this cycle and describe how the CNO cycle's strong temperature dependence makes it more prevalent in stars significantly more massive than the Sun compared to the proton-proton chain.

(a) Describe the essential physical conditions required for nuclear fusion to occur in the core of a main-sequence star.

(b) Explain how the process of nuclear fusion in the Sun's core contributes to its stability and its position on the main sequence.

(c) The proton-proton chain reaction is the primary fusion process in stars like the Sun. Consider the overall reaction:
$$4{}_{1}^{1}\text{H} \rightarrow {}_{2}^{4}\text{He} + 2e^{+} + 2\nu_{e} + 2\gamma$$
Given the rest mass of a proton is $$1.007825\text{ u}$$, and the rest mass of a helium-4 nucleus is $$4.002603\text{ u}$$.

(i) Calculate the mass defect in atomic mass units (u).

(ii) Determine the energy released in joules per reaction. (Assume $$1\text{ u} = 1.6605 \times 10^{-27}\text{ kg}$$ and the speed of light $$c = 3.00 \times 10^{8}\text{ m/s}$$).

A high-mass star (\(M > 8 M_{\odot}\)) undergoes different fusion stages compared to the Sun.
(a) Describe the stages of nucleosynthesis in a high-mass star leading up to the formation of an iron core.
(b) Explain why fusion reactions stop once iron is formed in the core.
(c) Discuss the process that occurs immediately after the iron core reaches the Chandrasekhar limit.