Calculating the explosive yield of an atomic bomb

[hoelmkjaer]

Homework Statement

I'm writing a paper on the Manhattan Project, and as part of this paper I am asked to show:
"... calculations that can help illustrate the explosive power of an atomic bomb compared to ordinary explosives."

Homework Equations

Released energy per fission:
Q = [tex]\Delta[/tex]m * c²

The Attempt at a Solution

I'm pretty sure I know how to do this. I just need to find a reliable source (e.g. not wikipedia) and find out how many fissions actually happened in the first atomic bombs (Little Boy and Fat Man), then multiply that amount by Q. Just want to make sure this is the proper way to do this. I figured I'd look up the yield for TNT, too, and then compare the energy released by the atomic bomb to an amount of TNT with equivalent energy.
Does anyone know where I might be able to find the amount of uranium, maybe even the enrichment level of it, used in Little Boy, and the same specifications for Fat man, along with the amount of each substance actually converted into energy during the explosion?

Thanks in advance
- Hoelmkjaer

 

[hoelmkjaer]

No one knows anything?
This is killing me... Has anyone got an idea? how I could illustrate the yield of a nuclear bomb compared to conventional explosives?

 

[gneill]

No one knows anything?
This is killing me... Has anyone got an idea? how I could illustrate the yield of a nuclear bomb compared to conventional explosives?

Compare the magnitude of the nuclear binding energy (per nucleon) with the typical binding energy of electrons. That is, the energy involved in nuclear reactions versus that involved in chemical reactions. Tables of binding energies are readily available for the elements.

Next look at the tabulated values for the energies for a specific fission. For example, the kinetic energy imparted to the fission products of plutonium (about 176 MeV per event) versus the energy released by a typical high explosive chemical reaction (this will involve a whole molecule per event -- so you can compare the energy released per unit of mass of the "reactants"). Semtex (Pentaerythritol tetranitrate) releases about 5810 kJ/kg.

 

[hoelmkjaer]

Thank you gneill. Never thought of a comparison at the molecular level, nor a comparison between nuclear binding energy and electron binding energy.

I recon I should be able show off some satisfactory calculations with this

 

[rwisz]

I would first like to commend your approach to finding reliable sources and comparing the energy released by an atomic bomb to that of ordinary explosives. This is an important aspect of understanding the destructive power of nuclear weapons.

To answer your question, the amount of uranium used in Little Boy was approximately 64 kg, with an enrichment level of 80%. The amount of plutonium used in Fat Man was about 6.2 kg, with an enrichment level of 89%. These numbers may vary slightly depending on the source, but they should give you a good estimate for your calculations.

In terms of the number of fissions that occurred in the bombs, it is estimated that Little Boy had around 140 fissions and Fat Man had around 500 fissions. Multiplying these numbers by the energy released per fission (Q) will give you an estimate of the total energy released by each bomb.

To compare this to the explosive power of TNT, you can use the equation for the energy released by TNT, which is 4.184 kJ per gram. So for example, if we take the estimated energy released by Little Boy (140 fissions * Q), which is approximately 15 kilotons of TNT equivalent, and convert it to grams, it would be equivalent to about 3.6 million grams of TNT.

It is important to note that these calculations are estimates and may vary depending on the exact specifications of the bombs and the energy released per fission. However, they provide a good understanding of the immense destructive power of nuclear weapons compared to ordinary explosives.