Question

Polonium-210 is a radioactive substance with a half-life of 138 days. If a nuclear facility is handling 300 grams of polonium-210, then how many grams of polonium-210 will be left in 270 days. Round your answer 4 decimal places and remember to use your labels.

Answer 1

The decay of a radioactive substance is represented by the formula A = A₀ e^-kt where A₀ is the initial quantity, A is the quantity left after t days and k is the constant of decay.

Here, A₀ = 300 grams, and A = 150 grams if t = 138. Hence, 150 = 300e^-138k , or e^-138k = 150/200 = 0.5.

Now, on taking natural log of both the sides, we get -138k = ln 0.5 = -0.69314718 so that k = 0.69314718/138 = 0.005022805656.

Thus, A = 300* e^{-0.005022805656t}. Now, when t = 270, we have A = 300* e^{-0.005022805656*270} =300*e^-1.356157527 = 300*0.257648886 = 77.2947 grams ( on rounding off to 4 decimal places).

Thus, 77.2947 grams of polonium-210 will be left in 270 days.