Q: Then half- life of a radioactive substance in 5000 years. In how many years, its activity will decay to 0.2 time of its initial value ? Given 1og_{10}5 = 0.6990

Sol: T = 5000 years,

N/N_{o} = 0.2 = 2/10 = 1/5

λ = (0.693 )/T = 0.693/5000

N/N_{o} = e^{-λt}

1/5 = e^{-λt}

5 = e^{λt}

log_{e}5 = λt

2.303 × 0.6990 = λt

t = (2.303 × 0.6990)/λ

t = (2.303 × 0.6990 × 5000)/0.693

t = 11614.6 years = 1.1615 × 10^{4} years.