How to Analyze a Plutonium-Based Atomic Bomb?

[Sarah Madsen]

< Mentor Note -- thread moved to HH from the technical physics forums, so no HH Template is shown >

Hello mates.

I was wandering how to analyze an atomic bomb, when the only information given, is that the bomb contains 5,6 kg plutonium, and is the same model as fat man.
Do you have any suggestions about formulas, and other things that can be analyzed through physics?
i was thinking about measuring the blast radius, and how long it takes for the exposed area to be radiation free, but can't find the proper formula and information.

Thanks in advance, English is not my main language, sorry for possible errors :)

 

[berkeman]

Hello mates.

I was wandering how to analyze an atomic bomb, when the only information given, is that the bomb contains 5,6 kg plutonium, and is the same model as fat man.
Do you have any suggestions about formulas, and other things that can be analyzed through physics?
i was thinking about measuring the blast radius, and how long it takes for the exposed area to be radiation free, but can't find the proper formula and information.

Thanks in advance, English is not my main language, sorry for possible errors :)

Welcome to the PF, Sarah.

Is this question for schoolwork? What reading and research have you been doing so far? If you can post links to your reading and ask specific questions about things you aren't understanding in that reading, that would be help...

 

[Sarah Madsen]

It´s a question for a school project. i got the basics in nuclear physics covered and knowledge about fission. It´s more the question about what to analyse? I thought about the blast radius and the energy that´s released, but is there other things I can calculate?

 

[mfb]

With only the amount of plutonium given you cannot do much, because you don't know how much of that plutonium will actually fission. You can try to find actual nuclear weapons of similar size to get an estimate. Once you have the yield, you can study effects of the explosion - blast radius, fallout, potential effects on a city, whatever.

 

[Sarah Madsen]

It says that the nuclear bomb is like the fat man bomb, but will this help in finding out how much of the plutonium that fission?

 

[mfb]

It is known (approximately) how much of the plutonium in Fat Man fissioned.

 

[Sarah Madsen]

So I need to find the energy released of a 6,4 kg plutonium, based on fat man.
First I tried to make an example with the fat man. so the fat man had Approx 1.176 Kilograms of plutonium converted to energy. Which means E=m*c^2 1
1,176*300000000^2=1,0584*10^17
which is 2457934990.4398 Kilotons, and fat man was about 20 kilotons.
What am i doing wrong?
Might be a stupid question, but i really don´t understand nuclear physics :(

 

[Sarah Madsen]

I think i need to find something like this, but how to convert 6,4 kg plutonium to this?

 

[mfb]

That's not what happens in nuclear fission.

so the fat man had Approx 1.176 Kilograms of plutonium converted to energy.

The plutonium is converted to fission products. Only a small fraction of its mass is released.

 

[Filip Larsen]

Perhaps if you knew the ... nuclear weapon yield ... of Fat Man you could scale the yield of the weapon you are analyzing to that of the Fat Man. You could of course also try to establish a theoretical upper limit of the yield as your last post indicates you are looking into, but then you still need to know how much of that maximum eventually end up as effective yield.

 

[Sarah Madsen]

I tried, but as you can see, the result is too high compared to the original amount of megatons.
I think I am missing the basics, but still looking for the answer.
I tried to calculate the Q of plutonium 239.
Q=8,4022*10^-13 J
But i don't know what to do next.

 

[Sarah Madsen]

so i found this formula.
Ekin after=Q+Ekin before.
Is this any good?

 

[Filip Larsen]

Perhaps you can try search for information on "nuclear weapon yield" and "plutonuim-239" and use that to get an overview of the processes involved? Perhaps you can even find an almost direct reference to how much energy pr kg that eventually is released during fission of Pu-239 and use that to get an upper limit of the yield. I still recommend that you look for the yield of Fat Man and compare this to how much Pu-239 it had, and then use this for the amount of Pu-239 you are supposed to analyse.

 

[mfb]

I tried to calculate the Q of plutonium 239.
Q=8,4022*10^-13 J
But i don't know what to do next.

That is the value for alpha decay. Again: fission is something different.

You can look up how much energy a plutonium atom releases in fission on average. You cannot calculate that value, you have to look it up (or directly use values for yields from elsewhere). Afterwards: How many plutonium atoms are there in 1 kg of plutonium?

 

[DrClaude]

so the fat man had Approx 1.176 Kilograms of plutonium converted to energy.

Where did you get that number?

Have you looked under "Specifications" on the Wikipedia page?
https://en.wikipedia.org/wiki/Fat_Man

 

[Filip Larsen]

And, just to spell it out, please note that Fat Man only achieved a fraction of the theoretical maximum yield for Pu-239 fission, which means you cannot just calculate the theoretical maximum yield and call that the effective yield of a similar Fat Man weapon. The exact fraction is not difficult to calculate once you have found the basic "performance numbers" mentioned in this thread.

 

[Sarah Madsen]

So i tried something else, but can i use it?
I dertirmined that it was plutinium239.

Where 6,4*10^3 is the mass.
Where 239,052158 is the mass/Unit before fission
and 239,046527 is the mass/Unit after.

 

[mfb]

Fission is not an alpha decay. You won't get any correct answer if you keep ignoring this fundamental error.

 

[Sarah Madsen]

Thanks for the help, i found the solution ;)

 

[Kaura]

Well according to Wikipedia the filling weight of the Fat Man was 6.4 kg
The yield of that model was 21.0 kt
I assume that for 5.6 kg of filling you would get 87.5% of that or about 18.375 kt
I maybe wrong as I am by no means versed in nuclear physics and the yield may not be linear

 

[Tom.G]

Thanks for the help, i found the solution ;)

Are you going to tell us what it is or are you going to keep us in suspense?