# Energy from White Dwarf Thermonuclear Runaway

• kvl214
In summary, the question asks to calculate the energy released when a 1 solar mass white dwarf converts 0.5 solar mass of carbon to iron. The attempt at a solution involves calculating the number of carbon particles, rest mass energies of carbon and iron, and using the ratio of 56/12 to determine the quantity of iron produced. However, it is important to preserve the nucleon count in nuclear reactions, and the correct approach would be to find the initial number of nucleons and the mass difference between carbon and iron per nucleon.
kvl214
Hello!

## Homework Statement

The question is "Calculate the energy released if a 1 solar mass white dwarf undergoes a thermonuclear runaway and converts 0.5 solar mass of carbon (A=12) to iron (A=56)."

I've only ever done nuclear equations with hydrogen fusion, with four hydrogens to one helium. But I don't know the reaction for carbon to iron, since it's not evenly divisible.

## Homework Equations

rest mass energy E = mc^2
energy released = E(reactants) - E(products)

## The Attempt at a Solution

I calculated the number of carbon particles from 0.5 solar masses -- 7.4e56 C particles
And the rest mass energies of carbon and iron -- C=1.1e4 MeV, Fe=5.2e4 MeV

Since 56/12 = 4.66, do we just use a fraction amount for carbon? So 4.66 C → 1 Fe ?

I just don't know where to go from here.

Any help would be greatly appreciated! Thanks

Nuclear reactions tend to operate slightly differently than chemical reactions.

Haven't you studied other nuclear reactions which occur in stars?

We only did hydrogen fusion, nothing with heavier elements...

What would you do for nuclear reactions?

Thanks!

I recalculated the rest mass energies with the atomic masses, since before i just used the integer number. So if i subtract 4.66*carbon energy from iron energy, does that work for the energy released in one reaction?

I also calculated that there are 1.6e56 reactions available from the mass of carbon...

I don't think you can take the 56/12 ratio to determine the quantity of iron produced. The nucleon count won't be preserved. Rather, reactions involve integral numbers of atoms. Of course, there are different pathways, but if the whole process only uses one pathway then there must be a whole number of carbon atoms to one iron atom.

haruspex said:
I don't think you can take the 56/12 ratio to determine the quantity of iron produced. The nucleon count won't be preserved. Rather, reactions involve integral numbers of atoms. Of course, there are different pathways, but if the whole process only uses one pathway then there must be a whole number of carbon atoms to one iron atom.

That's not right. You are thinking of chemistry. I think the only reasonable way to interpret the question is preserving the nucleon count. All you need to know about the reaction is that each nucleon will eventually wind up in an iron nucleus. So just find the mass per nucleon in carbon and use that to find the initial number of nucleons. Then find the mass difference between a nucleon in carbon and a nucleon in iron. And keep some extra decimal places around. The difference will be smallish.

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## What is "Energy from White Dwarf Thermonuclear Runaway"?

"Energy from White Dwarf Thermonuclear Runaway" refers to the process in which a white dwarf star, which is a remnant of a dead star, experiences a sudden and rapid increase in nuclear fusion reactions in its core. This results in a catastrophic explosion known as a thermonuclear runaway, releasing a tremendous amount of energy.

## How does a white dwarf star enter a thermonuclear runaway?

A white dwarf star enters a thermonuclear runaway when the mass of the star exceeds the Chandrasekhar limit, which is about 1.4 times the mass of our Sun. This causes the star's core to become hot and dense enough to ignite nuclear fusion reactions, leading to a chain reaction that rapidly increases in intensity.

## What are the potential consequences of a white dwarf thermonuclear runaway?

The consequences of a white dwarf thermonuclear runaway can be devastating. The explosion can release an enormous amount of energy, equivalent to millions of nuclear bombs, and can destroy the star and any surrounding planets. This event is known as a Type Ia supernova and can also release heavy elements into space, contributing to the formation of new stars and planets.

## Is it possible for a white dwarf thermonuclear runaway to occur in our Solar System?

No, it is not possible for a white dwarf thermonuclear runaway to occur in our Solar System. Our Sun is not massive enough to become a white dwarf and therefore cannot reach the Chandrasekhar limit. However, there are other white dwarf stars in our galaxy that could potentially experience a thermonuclear runaway.

## How does the energy released from a white dwarf thermonuclear runaway compare to other energy sources?

The energy released from a white dwarf thermonuclear runaway is among the most powerful events in the universe. It is estimated that a Type Ia supernova can release up to 10^44 joules of energy, which is equivalent to the energy output of our Sun over its entire lifetime. This is much more powerful than any man-made energy source currently available.

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