13.1  Explain the proton-proton chain process in which the Sun generates energy by converting hydrogen to helium.

In a multi-step process, four protons are fused together to produce first deuterium (a nucleus of one proton and one neutron), then ³He (two protons and one neutron), and finally ⁴He (two protons and two neutrons).  Along the way, other particles are produced - positrons, neutrinos, and photons - from the released energy.

13.7  Discuss the "solar neturino problem" and how this problem was solved.

The problem is that the measured flux of neutrinos coming from the Sun is 1/3 that which is expected from the hydrogen burned in the Sun.  Originally, the problem was thought to be with the model of the Sun, but recently we have discovered that the three types of neutrinos can interchange their identity, so some of the neutrinos from the Sun are turning into other types of neutrinos and the experiments are not sensitive to the other types of neutrinos.  

13.11  The Sun shines by converting mass into energy.  Show that the Sun produces 3.78 x 10²⁶ J of energy per second by expending 4.2 million tons (4.2 x 10⁹ kg) of mass per second.

E = mc² = 4.2 x 10⁹ kg x (3 x 10⁸ m/s)² = 3.78 x 10²⁶ J

13.12  Assume the Sun has been producing energy at a contant rate over its livetime of 4.5 billion years (1.4 x 10¹⁷ s).  
a.  How much mass has it lost creating energy over its lifetime?
b.  The present mass of the Sun is 2 x 10³⁰ kg.  What fraction of its mass has been converted into energy over the lifetime of the Sun?

a.  4.2 x 10⁹ kg/s x 1.4 x 10¹⁷ s = 5.88 x 10²⁶ kg.

b.  5.88 x 10²⁶ kg / 2 x 10³⁰ kg = 0.00029 or 0.029% of its mass (not much!!)