A piece of rock contains 10^20 atoms of a particular substance. Each atom has an expoentially distributed lifetime with a half-life of one century. How many centurites must pass before(adsbygoogle = window.adsbygoogle || []).push({});

there is about a 50% chance that at least one atom remains. What assumptions are you making?

answer:

so P (at least one survives past t) = P (no one does) = .5

now, I'm making the assumption that Prob of survival is so small and since n is huge, this follows a poisson disn.

thus .5 = P(k=0) = e^{-μ}

then μ = ln 5

now μ = np = 10^{20}* e^{-ln 2 t}. ln 2 is my parameter since half time is 1 century.

thus t = ln(10^{20}/ln 5) * (ln 2)^{-1}≈ 65 years

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# Exponential dsn. please check my work

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