Homeworks 5

Homework 5 due on 10/05/2009

Problem 1

The spectrum of a main-sequence star has strong hydrogen lines, weak lines of neutral helium, and weak lines of metals. What is the spectral type of the star? What is its approximate temperature? Suppose that the absorption lines of iron are much stronger than normal for a star of this spectral type. What could you conclude?

Problem 2

Compare the strong nuclear force to gravity and the electromagnetic force. Specifically, what kind of material or particle does each force act on? Are they short range or long range? Do they attract or repel? Are they strong or weak forces? If, as claimed, gravity is much weaker than the strong nuclear force, why do we notice gravity but not the nuclear force in our everyday lives?

Problem 3

The solar luminosity is $3.84x10^{33}$ erg/sec, derived from the fusion of hydrogen to helium. What mass of hydrogen is consumed each second to produce this energy and how many hydrogen nuclei are being turned into helium nuclei each second? How long does the sun live (assume that about 1/10 of all hydrogen gets burned).

Problem 4

Describe the CNO cycle of thermonuclear reactions, giving the formula for each of the steps in the chain. What do the symbols ${}^{12}C,{}^{13}C,e^{+},\gamma ,\!$ and $\nu ,\!$ mean in the formulae? Estimate the energy release per gram material. Estimate the life time of a star with 5$M_{\odot }$.

Problem 5

What are the most important factors determining which nuclear reactions take place in a star and how fast they take place? Why are they important? Why does the sun obtain its energy from the fusion of hydrogen to helium instead of some other nuclear reaction?