Question

Carbon-14 has a half-life of 5,730 years. How long will it take for 112.5 g of a 120.0-g sample to decay radioactively?
5,730 years
11,460 years
17,190 years
22,920 years

Answer 1

\(\Large \sf [A]_t=[A]_0*e^{-\frac{ln(2)t}{t_{1/2}}}\)


\(\Large \sf (120.0g -112.5 g)=120.0g *e^{-\frac{ln(2)t}{5,730 ~years}}\)


\(\sf \Large t=-\dfrac{5,730 ~years*{ln( \frac{(120.0g -112.5 g)}{120.0g})}}{ln(2)}=22386.48 ~years\)