Radioactive material obeys 1st order decay kinetics,
For 1st order reaction, we have
k = [tex] \frac{2.303}{t}Xlog \frac{\text{initial conc.}}{\text{final conc.}} [/tex]
where, k = rate constant of reaction
Given: Initial conc. 100, Final conc. = 6.25, t = 18.9 hours
∴ k = [tex] \frac{2.303}{18.9} X log \frac{100}{6.25} [/tex] = 0.1467 hours^(-1)
Now, for 1st order reactions: half life = [tex] \frac{0.693}{k} = \frac{0.693}{0.1467} [/tex] = 4.723 hours.
