NUCLEAR FUSION IN STARS
TOPICS | PARTICLES
STAR EVOLUTION

Q1) Draw out the diagram and label each particle , using the key.
 
 

Q2) Write equations for the second and third reactions. The first has been done for you.
 
 

Q3) Why is this a 'cycle' ?

On the earth, 150 million km from the sun , each square metre receives energy at the rate of 1.4 kW.

Q4) Calculate the total energy radiated by the sun per second.What has been assumed here ?
 

E = (Dm)c² , where Dm is the net mass difference.

 Mass-Energy Equivalence
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Q5) Explain why Dm = 4M_p - (M_a + 2 M_e).Show that this mass difference evaluates
to about 24.7 MeV.(Note: Most data books gives masses for isotopes , not nuclei - ie the relevant numbers of electrons are included. Compare Eg ¹H with proton mass)
 
 

Q6) Fom your answers to Q4 and Q5 show that the p-p cycle must occur approximately 10³⁸ times a second
 
 

Q7) The mass of the sun is 2x10³⁰kg. Assuming that initially all the mass of the sun was protons, how many does this correspond to ? If four are used up each time, show that the total possible energy release is about 1.2x10⁴⁵ J
 
 

Q8) Using your answers to Q4 and Q7 show that the lifetime of the sun could be 3x10¹⁸seconds . How many years is this ? Comment.

Self sustaining fusion reactions can only occur under conditions of extreme temperature and density. The core of the sun is believed to be at a temperature of about 1.5 x 10⁷ K which is sufficient for the p-p cycle to occur there.
 
 

Q9) How does this temperature compare with the ' threshold ' temperatures for the elementary particles that calculated in the 'Big Bang ' exercise ? Comment.

Hotter stars than the sun can sustain the Carbon cycle; this is pictured below:

Q10) There are six different nuclear reactions occurring in this cycle. Write full nuclear equations for them. One has been done for you .

Q11) Which species acts as a 'Catalyst' for the process? What is the net result of this cycle ? Calculate the energy output per cycle in MeV and comment.

Q12) When much of the hydrogen has been used up, the radiation pressure in the star will drop. Which force will now become important ? What effect will this have ?

A temperature of about 10⁸K is needed for helium fusion to begin an example is

Q13) Show that the energy evolved from this process is about 7.5 MeV

Other examples include ⁴ He +¹²C -> ¹⁶O and 2 ¹²C --> ²⁰Ne + ⁴He

Calculate the energy for these processes.

In heavier stars the temperature is higher. In stars of about 10 solar masses , the iron isotope ⁵⁶Fe is reached. This is the heaviest nucleus that can be formed in the core of stars by nuclear fusion.

Q14) The binding energy per nucleon is found by dividing its total binding energy by the number of nucleons it contains.

Show that the binding energy of deuterium is 2.2MeV.(Assuming it is made from a hydrogen isotope plus a neutron) and that its binding energy per nucleon is thus 1.1MeV
 

Q15) Suggest what nucleus gives the sharp spike on the graph. What nucleus will yield the maximum on the graph ? What consequences does this have for nuclear fusion and element synthesis inside stars ?
 

Q16) Show that for your chosen maximum element that the binding energy is 492.5 MeV and that the binding energy per nucleon is 8.8MeV. State clearly any assumptions you make. Repeat this calculation for a different element in the 'Fission' range and comment.

Q17) Try to find out how heavier nuclei are made. Encarta and Redshift 2 software are useful.

Q18) The isotope of Bismuth ²⁰⁹Bi contains the largest known binding energy. Calculate this value and show that its binding energy per nucleon is considerably less than 8.8MeV.

Q19) This bismuth isotope is thought to be the heaviest that can form in the cores of stars. Why ? Isotopes of masses up to 260 amu may form. Where ? and why ?

Q20) Try to find out what you can about Solar Neutrinos and their importance.