Plutonium core of second nuclear bomb
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The following quantities appear in the problem:
Masse \(m\) / Volumen \(V\) / molare Masse \(M\) / Stoffmenge \(n\) / Radius \(r\) / Dichte \(\varrho\) /
The following formulas must be used to solve the exercise:
\(\varrho = \dfrac{m}{V} \quad \) \(V = \dfrac{4}{3}\pi r^3 \quad \) \(m = nM \quad \)
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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. How many single plutonium atoms did it consist of? One avoirdupois ounce is .g one inch is .cm.
Solution:
Geg rho rO r M MO M r RO R 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^ r V m mass. So the sphere consisted of n fracmM frac fracpirho r^M fracmM n N n sscNA frac fracpirho r^M sscNA n ncNA N plutonium atoms. n fracpirho r^M n N fracpirho r^ sscNAM N
The plutonium rO MO core of the second nuclear bomb to be detonated in a war nicknamed Fat Man had a radius of RO. How many single plutonium atoms did it consist of? One avoirdupois ounce is .g one inch is .cm.
Solution:
Geg rho rO r M MO M r RO R 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^ r V m mass. So the sphere consisted of n fracmM frac fracpirho r^M fracmM n N n sscNA frac fracpirho r^M sscNA n ncNA N plutonium atoms. n fracpirho r^M n N fracpirho r^ sscNAM N