Question

$1.0g$ of ${}_{79}^{198}Au$ $(t_{1/2}=65hours)$ by $\beta$-emission to produce mercury.
(a) Write the nuclear reaction for the process.
(b) How much mercury will be present after $260$ hours?

Answer 1

(a) ${}_{79}^{198}Au{⟶}_{80}^{198}Hg{+}_{-1}^{0}e$
(b) Number of half lives in $260$ hours $=\frac{260}{65}=4$
Amount of gold left after $4$ half lives $={\left(\frac{1}{2}\right)}^4=\frac{1}{16}g$
Amount of gold disintegrated $=1-\frac{1}{16}=\frac{15}{16}g$
Amount of mercury formed $=\frac{15}{16}=0.9375g$