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 millisecon^{1})
 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.
Simulator Settings
The simulator is based on Uranium235. When and U235 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>
Statistics
Uranium235
 Atomic weight
 (so 235g of U235 is 1 mole)
 Density
 g/cm^{3}
 Fission energy (per atom)
 MeV (megaelectronvolts)
TNT
 Energy of 1 ton
 GJ
Constants
 Avogardo Number (A)
 /mol (Number of atoms in 1 mole of a substance)
Conversions
 1 MeV
 J
 Number of U235 atoms/g
 /g
 Energy of 1g of U235
 GJ
 To work out how many grams of U235 you would need to create a blast of energy E you can use
 Tons
 1 ton = 1,000 Kg
Unit prefixes
Symbol  Name  Factor  Power 

P  Peta  1,000,000,000,000,000  10^{15} 
T  Tera  1,000,000,000,000  10^{12} 
G  Giga  1,000,000,000  10^{9} 
M  Mega  1,000,000  10^{6} 
K  Kilo  1,000  10^{3} 
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 U235  Number of reaction generations  Energy  Comparison 

1 ug The size of an animal cell. 
55  1MJ  1 standard stick of dynamite (190g of nitroglycerine). 
50 mg The size of a flea. 
67  4 GJ or 1 ton TNT 
Would form a crater around 100m diameter. 
1 g The size of a small 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. 
81  62 TJ or 15 Kilotons of TNT 
The Atomic Bomb (Little Boy) dropped on 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. 
87  2 PJ or 500 Kilotons of TNT 
Modern W87 thermonuclear warhead. Small enough to fit in a backpack! This is the largest theoretical size of an atomic fission reaction. 
–  –  42 PJ or 10 Megatons of TNT 
Typical blast of a big volcano erupting. 
–  –  209 PJ or 50 Megatons TNT 
Largest thermonuclear device ever made. 
–  –  4.2×10^{20} J or 100 Teratons TNT 
The Chicxulub Meteor impact believed to be the cause of the mass extinction of the dinosaurs. 

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. ↩︎
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