My son was looking at the Atomic Bomb (fission bomb) for his project. It's all very well to understand how the chain reaction works and to look up facts about blast yields, but it's much harder to portray the awesome power involved in a real context. For example, a blast equivalent to 1 kiloton of TNT is clearly a big bang but most people have little concept of what it actually means; and indeed how much bigger is a 1 megaton blast? It's all a bit hard to imagine.

To try and portray a feel for the enormous energy released from nuclear fission I think it is important to understand 3 basic concepts:

  • The fission chain reaction grows exponentially (that is, it's growth is accelerating all the time - it is not constant. The Hiroshima bomb took only around 81 generations)
  • The chain reaction occurs very quickly (100 generations will take less than 1 millisecon1)
  • The amount of energy released in some real world context to give some idea of how much energy can be released from an amount of fissionable material.

To help understanding of these I wrote a simulator to show the rapid/exponential growth (doubling) of the chain reaction.

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Simulator Settings

The simulator is based on Uranium-235. When and U-235 atom splits it releases an average of 2.4 neutrons. Not all these neutrons will cause a further fission so I have approximated the reaction rate to 2 times per generation. Also, I have not taken into account fuel being used up and the expansion of the fuel; both of which would slow the reaction. However, since the simulation is obliterated within the first 25 generations these effects should be negligible (I reckon they would only start making a difference at around 50 generations for a fission bomb).

The energy at each point is represented by the colour; with reds showing only a handful of reactions, through to oranges and finally yellows that represent large amounts of energy from a great many number of reactions.

The simulator is written in JavaScript which is not the most efficient language to use for any mathematical modeling and with doubling the number of atoms per generation we very quickly grind to a halt. So I only double the number of fission atoms until there are 1024. After that I freeze the number of fission events per generation at 1024 and double the resulting atom or energy release size instead. Also the atoms are represented as squares (since rendering circles is far too expensive computationally). Both of these lead to the simulation taking on a squarish shape during the later generations.

You are welcome to embed my simulator in your site, use the code below. Please give me an acknowledgement and a link back to icedaddy.net.

<iframe width="730" height="470" src="http://embed.icedaddy.net/atomic/" frameborder="0"></iframe>

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Statistics

Uranium-235

Atomic weight
235 (so 235g of U-235 is 1 mole)
Density
19.1 g/cm3
Fission energy (per atom)
200 MeV (megaelectronvolts)

TNT

Energy of 1 ton
4.184 GJ

Constants

Avogardo Number (A)
6.02214e+23 /mol (Number of atoms in 1 mole of a substance)

Conversions

1 MeV
1.60218e-13 J
Number of U-235 atoms/g
Atoms/g /g
Energy of 1g of U-235
82 GJ
To work out how many grams of U-235 you would need to create a blast of energy E you can use
Tons
1 ton = 1,000 Kg
738

Unit prefixes

Symbol Name Factor Power
P Peta 1,000,000,000,000,000 1015
T Tera 1,000,000,000,000 1012
G Giga 1,000,000,000 109
M Mega 1,000,000 106
K Kilo 1,000 103
m milli 0.001 10-3
u micro 0.000,001 10-6

Unts

Symbol Name Type
g grams Mass
J Joules Energy
m Metres Length

I also ran a few numbers to try and get the power involved into something that can be related and imagined. The figures given here are a bit rough and ready and don't take into account many practical factors. However, they do serve to give a good indication and comparison of the levels of energy involved.

Quantity of U-235 Number of reaction generations Energy Comparison
1 ug
The size of an animal cell.
Animal cell		 55 1MJ 1 standard stick of dynamite (190g of nitroglycerine). Dynamite
50 mg
The size of a flea.
Flea		 67 4 GJ
or
1 ton TNT		 Would form a crater around 100m diameter.
1 g
The size of a small pebble.
Pebble		 71 82 GJ
or
20 tons TNT		 A small bedroom packed floor to ceiling with TNT. The blast would completely obliterate the house and many others in the street.
1 Kg
The size of a tennis ball.
Tennis ball		 81 62 TJ
or
15 Kilo-tons of TNT		 The Atomic Bomb (Little Boy) dropped on Hiroshima. Hiroshima
Actually the Hiroshima bomb contained around 50Kg of Uranium but only a very small amount of this actually exploded before the Uranium was dispersed enough for the chain reaction to stop.
50 Kg
The size of a football.
Football		 87 2 PJ
or
500 Kilo-tons of TNT		 Modern W-87 thermonuclear warhead. Small enough to fit in a backpack! W-87 This is the largest theoretical size of an atomic fission reaction.
- - 42 PJ
or
10 Mega-tons of TNT		 Typical blast of a big volcano erupting. Volcano
- - 209 PJ
or
50 Mega-tons TNT		 Largest thermonuclear device ever made.
- - 4.2x1020 J
or
100 Tera-tons TNT		 Meteor The Chicxulub Meteor impact believed to be the cause of the mass extinction of the dinosaurs.

  1. 100 generations in 1 millisecond is what I worked out with my quick and dirty (and probably not very accurate) calculations; but it is a reasonable estimate and helps understanding of the rapid speed of the energy release. ↩︎