ShmoopTube

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Here’s your Shmoop du jour, brought to you by world domination.

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How hard is that to pull off, anyway? [Man dressed in battle gear preparing a plan for world domination]

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…We’re asking for a friend.

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Here’s today’s question:

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As evil masterminds, we are on the verge of learning how to make kryptonite so that we

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can render Superman powerless. [Krptonite and Superman appears]

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We learn that we need 18 g of a radioactive isotope of krypton, krypton 85, to complete

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our recipe for world domination.

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Krypton 85 has a half-life, t one half, of about 10 years, and it only exists on the

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planet Neptune.

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It will take us 20 years to return from Neptune back to Earth.

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How much krypton 85 will we need to collect from Neptune to have enough left to take over the world?

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And here are your potential answers:

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Superman is strong, fast, and pretty darn handsome, but even he can be defeated by a [Superman makes robbers disappear]

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chemical compound. [Masked man shows Superman kryptonite]

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So you can feel better about AP Chem being your one weakness.

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You’re in good company.

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To solve today’s problem, we need to remember that the half-life is the amount of time it

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takes for half of the radioactive compound krypton 85 to decay.

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After each half-life passes, the amount of krypton 85 left has decreased by a factor

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of two.

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Not to be mixed up with the time period “half of your life,” which is how long we were [Man sat waiting at a table]

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waiting for Adele to release her new album. [Adele singing]

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No hard feelings, Adele.

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It was worth the wait.

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Anyway, the half-life of krypton 85 is 10 years, but the journey back from the planet

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Neptune will take 20 years.

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It will also take us 20 years to get to Neptune…

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Forty years is a perfectly reasonable amount of time to take to surprise somebody, right? [Superman grows a beard]

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Nobody can catch on when you’re moving that quickly!

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So the 20 year journey home is equal to two half-lives of Krypton 85.

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During this time, the amount of krypton 85 will be cut in half twice, so the amount remaining [Masked man holding krypton]

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when we get back to Earth will be only one quarter of the amount we had when we left

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Neptune.

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We’ll have to gather exactly four times as much as we need, but absolutely no more. [A small and large piece of krypton]

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We might be evil, but we don’t have to be wasteful. [Masked man drops soda can in the trash]

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Since we’ll need 18 grams of krypton 85 on earth, and we have to gather four times

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as much on Neptune, that means we have to collect 4 x 18 = 72 grams.

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That means D is the correct answer.

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Now all that’s left is to execute our brilliant secret plan.

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Good thing Superman doesn’t watch Shmoop. [Superman watching Shmoop on TV]

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Or does he…? Dang it.

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