Answer:
16 mg
Step-by-step explanation:
[tex]N_0[/tex] = Initial mass of sample = 540 mg
t = Time taken = 2 years
[tex]t_{1/2}[/tex] = Half life of isotope
N = Final mass of sample = 300 mg
Radioactive decay is given by
[tex]N=N_0e^{-\dfrac{\ln 2}{t_{1/2}}t}\\\Rightarrow \ln\dfrac{N}{N_0}=-\dfrac{\ln 2}{t_{1/2}}t\\\Rightarrow t_{1/2}=-\dfrac{\ln2}{\ln\dfrac{N}{N_0}}t\\\Rightarrow t_{1/2}=-\dfrac{\ln2}{\ln\dfrac{300}{540}}2\\\Rightarrow t_{1/2}=2.358\ \text{years}[/tex]
In 2021 the number of years passed from 2009 would be 12 years
[tex]N=N_0e^{-\dfrac{\ln 2}{t_{1/2}}t}\\\Rightarrow N=540e^{-\dfrac{\ln 2}{2.358}12}\\\Rightarrow N=15.86\approx 16\ \text{mg}[/tex]
The expected mass of the sample in the year 2021 would be 16 mg.
