Activity of Fat Mans Plutonium core
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Exercise:
The plutonium rO MO core of the second nuclear bomb to be detonated in a war nicknamed Fat Man had a radius of RO. What was its activity given that it was made of pure isotopePu with TO half-life? One avoirdupois ounce is .g one inch is .cm.
Solution:
Geg rho rO r M MO M r RO R T TO T GesNumber/amountN The sphere had V frac pi r^ frac pi qtyR^ V volume and therefore m rho V rho frac pi r^ frac pi rho r^ frac pi r qtyR^ m mass. So the sphere consisted of n fracmM frac fracpirho r^M frac fracpi r qtyR^M n N n sscNA frac fracpirho r^M sscNA frac fracpi r qtyR^M ncNA N plutonium atoms with A lambda N lambda frac fracpirho r^M sscNA A approx AS AP activity. A frac fracpirho lambda r^M sscNA AS AP
The plutonium rO MO core of the second nuclear bomb to be detonated in a war nicknamed Fat Man had a radius of RO. What was its activity given that it was made of pure isotopePu with TO half-life? One avoirdupois ounce is .g one inch is .cm.
Solution:
Geg rho rO r M MO M r RO R T TO T GesNumber/amountN The sphere had V frac pi r^ frac pi qtyR^ V volume and therefore m rho V rho frac pi r^ frac pi rho r^ frac pi r qtyR^ m mass. So the sphere consisted of n fracmM frac fracpirho r^M frac fracpi r qtyR^M n N n sscNA frac fracpirho r^M sscNA frac fracpi r qtyR^M ncNA N plutonium atoms with A lambda N lambda frac fracpirho r^M sscNA A approx AS AP activity. A frac fracpirho lambda r^M sscNA AS AP