WEBVTT
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This is College Physics Answers
with Shaun Dychko.
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How many plutonium-239 nuclei must fission
to produce a 20.0 kiloton yield in a bomb?
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So we will convert the kilotons into
joules by multiplying by
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4.2 times 10 to the 12 joules per kiloton
and that is 8.4 times 10 to the 13 joules.
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We are told that each fission produces
an energy of 200 megaelectron volts
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and we will convert that into joules
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by writing 200 times 10 to the 6
electron volts per fission
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times 1.602 times 10 to the minus
19 joules per electron volt
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and that is 3.204 times 10 to the minus
11 joules per fission
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and we are fissioning plutonium-239.
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So the number of nuclei then will be
1 nucleus per fission—
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I mean this is maybe a bit obvious
but I wrote it down anyway—
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times 1 fission for every 3.204 times
10 to the minus 11 joules
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and then multiplied by
the number of joules
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and writing the fractions this way,
we can see how the units cancel
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giving us units of number of nuclei
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and that's 2.62 times 10 to the 24 nuclei
of plutonium-239.
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How much mass would that
number of nuclei have?
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So we take that number of nuclei,
convert it into moles
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by multiplying by 1 mol for every 6.0221
times 10 to the 23 nuclei—
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this is Avogadro's number—
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and then look up in our appendix at
the end of the textbook
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for the molar mass which is
239.052 grams per mol
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that's 1040 grams or 1.04 kilograms.