Answer:The half-life of an element is 20 days.
Explanation:
Radioactive decay of reaction follows first order kinetics, and half life of an element is given as:
[tex]t_{\frac{1}{2}}=\frac{0.693}{\lambda }[/tex]
[tex]\lambda [/tex]= Decay constant
Decay constant of an element= [tex]\lambda = 3.411\%=0.03411 (day)^{-1}[/tex]
[tex]t_{\frac{1}{2}}[/tex] = half-life of an element
[tex]t_{\frac{1}{2}}=\frac{0.693}{0.03411 (day)^{-1}}[/tex]
[tex]t_{\frac{1}{2}}=20.31 days\approx 20 days[/tex]
Hence, the half-life of an element is 20 days.
