# Nuclear fusion

i got a atronphysics question that i have a hard time to solve it:

In the most massive stars, nuclear fusion continues until iron-56 is formed in the core. consider the net process, which is to take 56 hydrogen atoms and turn them into one iron atom.
a, how much enegry is released per atom?
the answer i get is 10ev per atom, i thought this is not a correct answer.

b. an iron core of a massive star has is typically 2 solar masses in size.how much energy has the star generated in forming this core, through fusion?
the answer i get is 3.81*10^39 J

c.if the star shines with a luminosity of 100,000 times that of the sun, how long do you expect it to live?
i have no idea how to solve question c...

any help is appreciated......

## Answers and Replies

mgb_phys
Science Advisor
Homework Helper
In the most massive stars, nuclear fusion continues until iron-56 is formed in the core. consider the net process, which is to take 56 hydrogen atoms and turn them into one iron atom.
Is not really as simple as that, but you should expect a small positive value. That is forming iron is (just) energetically favourable.

b. an iron core of a massive star has is typically 2 solar masses in size.how much energy has the star generated in forming this core, through fusion?
the answer i get is 3.81*10^39 J
Number of moles of iron * answer to a .

c.if the star shines with a luminosity of 100,000 times that of the sun, how long do you expect it to live?
In a very simple picture just take the number of Joules you found above and the sun's luminosity and divide.

dynamicsolo
Homework Helper
i got a atronphysics question that i have a hard time to solve it:

In the most massive stars, nuclear fusion continues until iron-56 is formed in the core. consider the net process, which is to take 56 hydrogen atoms and turn them into one iron atom.
a, how much enegry is released per atom?
the answer i get is 10ev per atom, i thought this is not a correct answer.

Was this supposed to read '10 MeV per atom'? Also, is that per hydrogen nucleus? If so, it is in the right neighborhood, though slightly high.

You'll need the following information:

the 56 hydrogen atoms have protons for nuclei, so you start out with

56 x mass of a proton (mass of proton: 1.007 276 atomic mass units)
[see, for instance, http://physics.nist.gov/cgi-bin/cuu/Value?mp|search_for=atomnuc! ];

through the fusion history of the stellar core, these get converted into a single Fe-56 nucleus, having 26 protons and 30 neutrons and a negative binding energy, so the
mass of this nucleus is actually

mass of Fe-56 nucleus: 55.92066 atomic mass units
[see, for instance, http://www.cartage.org.lb/en/themes/Sciences/Chemistry/NuclearChemistry/NuclChemIndex/NuclearBindingEnergy/NuclearBindingEnergy.htm [Broken] ] ;

the atomic mass unit has an energy equivalent of 931.494 MeV
[see http://physics.nist.gov/cgi-bin/cuu/Value?uev ] .

You will need to calculate the change in mass of the group of protons in becoming a single Fe-56 nuclei in amu and then convert that to MeV. If you divide this by the 56 hydrogen nuclei, you will get a figure somewhat lower than 10 MeV/proton. (I'm not clear on how much precision you are being asked for...)

b. an iron core of a massive star has is typically 2 solar masses in size.how much energy has the star generated in forming this core, through fusion?
the answer i get is 3.81*10^39 J

This figure is very low. Find the number of protons in 2 solar masses (close to 2 · 10^30 kg.) and multiply this by the energy release per proton from part (a), then convert this to Joules.

As a rough check, the gravitational binding energy of a uniform sphere is

-0.6 · [ G(M^2)/R ] .

For the 2-solar mass stellar core near the end of its fusion lifetime, its radius will be somewhat small than a white dwarf star, say, 3000 km. This value will be an underestimate, since the actual core is rather denser near its center than at its periphery.

c.if the star shines with a luminosity of 100,000 times that of the sun, how long do you expect it to live?

mgb_phys has given the method for an estimate of the stellar lifetime. Since we are looking at the most massive stars here, you should get a figure not larger than a few million years.

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