the half life of polonium is 139 days. you have a brand new sample of polonium that will not be useful to you after 80% of the material hasd

Question

the half life of polonium is 139 days. you have a brand new sample of polonium that will not be useful to you after 80% of the material hasdistegraded. For how many days will you be able to use the polonium?

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Savannah 5 months 2021-09-03T18:55:46+00:00 1 Answer 0 views 0

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    2021-09-03T18:56:50+00:00

    The half-life of Po is 139 days, so its decay rate is

    0.5 = e^(139k)  ==>  k = ln(0.5)/139

    After some time t, 80% of the material will have decayed and you’ll be left with a sample 20% of its original mass:

    0.2 = e^(kt)  ==>  t = ln(0.2)/k = ln(0.2)/ln(0.5) * 139 = 322.748

    so your sample is usable for about 323 days.

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