How long will a star remain stable by burning Silicon

[TheTourist]

Given the semi-empirical mass formula for the binding energy of a nucleus is
B(Z,A)=a₁A-a₂A^2/3-a₃Z²/A^1/3-a₄(Z-N)²/A+delta(Z,A)

calculate the energy released in the reaction ²⁸Si +⁴He --> ³²S + gamma.

Hence find how long silicon burning will sustain a massive star which has 1M_o of silicon in its core and a luminosity of 10⁵L_o. Comment on the answer you get and is it the right answer, if not, why not?

Take the binding energy of Helium-4 to be 26.7MeV which is not accurately predicted by this formula

Ok, i calculated that energy released in the reaction is about 9.6MeV. I then found the number of silicon nuclei in the core, by dividing total mass by mass of one silicon nuclei, and hence the total energy which is 6.48x10⁴³J.

To find the time I divided this total energy by the luminosity which gave 1.71x10¹²s, or 54,191 years.

The reason I think this is the wrong answer is because it is not taking into account the iron core that is produced, which will reach the Chandrasekar limit before all of the silicon is fused. Hence the answer is too large.

Can someone please check my method and final answer are reasonable; I know the answer is a lot bigger than the actual value.

Homework Statement

Homework Equations

The Attempt at a Solution

 

[NateD]

Ok, i calculated that energy released in the reaction is about 9.6MeV. I then found the number of silicon nuclei in the core, by dividing total mass by mass of one silicon nuclei, and hence the total energy which is 6.48x1043J.To find the time I divided this total energy by the luminosity which gave 1.71x1012s, or 54,191 years.The reason I think this is the wrong answer is because it is not taking into account the iron core that is produced, which will reach the Chandrasekar limit before all of the silicon is fused. Hence the answer is too large.Can someone please check my method and final answer are reasonable; I know the answer is a lot bigger than the actual value.