Question

If a substance has a half life of 58 years and starts with 500 g radioactive, how much remains radioactive after 30 years?

Answer 1

Answer:

A = 349 g.

Explanation:

Hello there!

In this case, since the radioactive decay kinetic model is based on the first-order kinetics whose integrated rate law is:

$A=Ao*exp(-kt)$

We can firstly calculate the rate constant given the half-life as shown below:

$k=\frac{ln(2)}{t_{1/2}} =\frac{ln(2)}{58year}=0.012year^{-1}$

Therefore, we can next plug in the rate constant, elapsed time and initial mass of the radioactive to obtain:

$A=500g*exp(-0.012year^{-1} *30year)\\\\A=349g$

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