Radioactive elements obey 1st order kinetics,
For 1st order reaction, relation between rate constant (k) and half life [t(1/2)] is,
k = [tex] \frac{0.693}{t(1/2)} = \frac{0.693}{5750} = 1.205 X 10^-^4 hr^-^1 [/tex]
Also, for 1st order reaction, we have
t = [tex] \frac{2.303}{k} log \frac{\text{initial conc.}}{\text{final conc.}} [/tex]
Given that: the bones from a mastodon had lost 78.5% of their C14,
∴ initial conc. of C14 = 100%, conc. of C14 left after time 't' = 21.5%
∴t = [tex] \frac{2.303}{1.205 X 10^(-4)} log \frac{\text{100}}{\text{21.5}} [/tex] = 1.2758 X 10^4 hours
