One Gram Killed Hiroshima
Albert Einstein's famous mass-energy equivalence principle, E = mc2 lead to the eventual development of atomic weapons.
About a month ago I wrote a post on the first atomic bomb which was a plutonium-239 implosion device which was followed shortly thereafter by the bombing of the city of Hiroshima.
This post is not about the moral question of the Hiroshima bombing but instead is just about some interesting aspects of the physics.
Specifically, how much matter had to disappear to create the blast that leveled Hiroshima?
TNT Equivalence
The phrase term TNT equivalent is a term used to compare the power of a fission powered bomb or a fusion powered bomb to a more conventional chemically powered bomb such as you would get from TNT.
In this correlation a kiloton of TNT has been determined to be equal to 4.184 terajoules of energy. The metric prefix 'tera' means 1000 billion or one trillion. In scientific notation this is 1012.
So there are 4.184 1012 joules of energy released in a kiloton blast.
The Hiroshima bomb was estimated to be 16 kilotons. Doing the math this equates to 67 x 1012 joules of energy.
Mass Equivalence
A small amount of mass converts to a large amount of energy basically because of the c2 term where 'c' is the speed of light which equals ~300,000,000 metres per second.
Re-arranging the mass-energy equation E = mc2 and solving for m we get m = E/c2 .
Units Analysis: Energy is measured in joules and a joule is 1 kg·m2/s2. Dividing it by c2 means you are dividing by m2/s2. The units cancel out to leave just kg (kilograms).
So, doing the math once again we get:
m = 67 x 1012 joules/(300,000,000 m/s x 300,000,000 m/s) = 0.000744 kg, or 0.74 g.
Since the estimate of the power of the Hiroshima bomb is believed to be fairly inaccurate we can simply round that answer up 1 gram (hence the title of my post).
The Tsar Bomba
The largest bomb ever exploded was done by the Russians and it was called the Tsar Bomba. The word Tsar means Czar which also means Emperor (I guess). So in English I presume that this translates to 'Emperor Bomb' or 'King Bomb'.
The power of this bomb was truly massive and the blast was estimated to be around 50 megatons (>3,000 times more powerful than the Hiroshima bomb).
Doing the math yet again: 50 megatons divided by c2 gives us about 2.3 kg of mass disappeared in that particular bomb and then re-appeared as energy to produce the blast.
The fireball from the blast was 8 km (5 miles) in diameter and the mushroom cloud reached 64 km (40 miles) into the atmosphere. This particular bomb is worth devoting an entire post just to it alone.
Closing Words
Putting aside the horror of Hiroshima and Nagasaki, I always find it amazing how much energy can be extracted from so little mass.
It's best that this awesome power be used in peaceful and beneficial pursuits like nuclear reactors although not everyone agrees on this topic as well.
Thank you for reading my post.
Post Sources
https://en.wikipedia.org/wiki/Atomic_bombings_of_Hiroshima_and_Nagasaki
https://en.wikipedia.org/wiki/TNT_equivalent
https://en.wikipedia.org/wiki/Mass%E2%80%93energy_equivalence
https://en.wikipedia.org/wiki/Joule
https://en.wikipedia.org/wiki/Trinity_%28nuclear_test%29
https://en.wikipedia.org/wiki/Tsar_Bomba
I wrote a style guide (link here) for STEM posts that you might find interesting (or not, it's up to you).
This is really scary...
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Very interesting. I haven't done the math , but if I remember correctly you need around 25kg of Uranium to achieve a critical mass. Following your argument, only a fraction of this mass is then converted into energy. What happens to the rest?
It gets spread out all over Hell's half-acre.
😲 😲 😲 😲 😲 😲 😲 😲 😲 😲 😲 I hate physics and math 😲 😲 😲 😲 😲
Sorry to hear that. There's more to physics than a-bombs though.
Have an upvote nevertheless for your fearless honesty.
one day a country will make a bomb that will distroy all world once. sad to knowing about the wars and latest arms.
I didn't imagine such difference in mass between Tsar and Little Boy.
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