This is a question in astrophysics class, please answer all the sub-questions. E
ID: 2078169 • Letter: T
Question
This is a question in astrophysics class, please answer all the sub-questions.
Explain the following questions: (a) From classically calculation, to make hydrogen burning (fusion), the proton must have sufficient energy to overcome the Coulomb barrier so that the two protons can be as close as 10^-13 cm to make fusion. However, it needs the temperature as high as 10^10 K, which is much higher than the temperature at the core of main sequence stars (only 10^7 K). How the fusion can be processed inside a star? (b) Explain why it needs higher temperature to process CNO cycle than pp chain.Explanation / Answer
(a) The calculation of the Coulomb barrier determines the average energy per proton needed for fusion. However these energies are distributed according to the bell shaped Maxwell-Boltzmann distribution. Within its long tail there is a sufficiently large number of particles whose energy is much larger than the average and thus enough to initiate fusion. It is not necessary for the incident protons to have sufficient energy to overcome the Coulomb barrier entirely. Due to the wave-particle duality and the statistical probabilities of the properties of very small particles, the protons can also pass through the barrier by a phenomenon known as quantum tunnelling, provided the barrier height is not too high above the kinetic energy of the incoming particle.
(b) The pp-chain is governed by the very slow rate of the first reaction, while the CN cycle is governed by the amount of C12 available in the star. The CN-cycle requires higher temperatures than the pp-chain, because a higher Coulomb potential is involved. It turns out that it is more important on the upper main sequence (M > Ms) while the pp-chain is more important on the lower main sequence (M<Ms). The consequence of this is that stars can burn Hydrogen about 10 times longer than they can burn Helium.
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