Answer to Question #188989 in Atomic and Nuclear Physics for Angie Quintanar

Question #188989

A 100 g sample of a radioactive isotope has a half life of 2 days. After 6 days how many grams of the original radioactive isotope are left?


1
Expert's answer
2021-05-04T12:07:42-0400

The formula of decay has form "N(t) = N_0\\cdot 2^{-t\/T_{1\/2}}" , where "N_0" is the initial number of atoms, "t" is the time interval and "T_{1\/2}" is the half-life time.

Therefore, "\\dfrac{N(t)}{N_0} = 2^{-t\/T_{1\/2}}" .

In our case "t = 6^d, \\; T_{1\/2} = 2^d," so "\\dfrac{N(t)}{N_0} = 2^{-6\/2} = \\dfrac18," so only one eighth of the initial number of radioactive atoms will be left. Therefore, only "100\\cdot\\dfrac18 = 12.5" g will be left.


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