# Calculating the explosive yield of an atomic bomb

#### hoelmkjaer

1. 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."

2. Homework Equations
Released energy per fission:
Q = $$\Delta$$m * c2

3. 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

Last edited:
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#### 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

Mentor
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

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