Question

The half life of a radioactive substance is $5000$ years. The number of years after which its activity will decrease to $0.2$ times of its initial value is:
(log${}_{10}5=$ 0.6990)

• A. $1.02$ $\times {10}^5$ years
• B. $2.34$$\times {10}^6$ years
• C. $2.06$$\times {10}^2$ years
• D. $1.16$ $\times {10}^4$ years

Answer 1

The correct option is D $1.16$ $\times {10}^4$ years

$t_{1/2}=5000yr$

$N=\left(0.2\right)N_0$

$R=\left(0.2\right)R_0$

$ln\frac{N_0}{.2N_0}=\left(\frac{.693}{5000}\right)t$

$t=1.16\times {10}^{4}yr$