Question

The half-life of nickel-63 is 92 years. The amount of nickel-63 in a sample is .670 g. How much nickel-63

would be left after 460 years?

Answer 1

`\textit{Amount for Exponential Decay using Half-Life} \\\\ A=P\left( (1)/(2) \right)^{(t)/(h)}\qquad \begin{cases} A=\textit{current amount}\\ P=\textit{initial amount}\dotfill &\stackrel{grams}{0.67}\\ t=\textit{elapsed time}\dotfill &\stackrel{years}{460}\\ h=\textit{half-life}\dotfill &\stackrel{years}{92} \end{cases} \\\\\\ A=0.67\left( (1)/(2) \right)^{(460)/(92)}\implies A=0.67\left( (1)/(2) \right)^5\implies A\approx 0.021~grams`