Question

half life of radioactive substance is 100 years. calculate in how many years the acivity will decay to 1/10 of its initial value​

Answer 1

Answer:

$\implies \rm R = \dfrac{R_0}{10}$

$\implies \rm {T_\frac{1}{2} } = 100\;years$

$\implies \rm{R_0 \;is\;the\;initial\;activity}$,

Using the formula,

$\implies \boxed{\rm \dfrac{0.693}{T\frac{1}{2} } *t = ln\dfrac{R_0}{R}}$

$\rm \therefore \dfrac{0.693}{100} *t = ln(10)$

$\rm \implies \;t = \dfrac{100}{0.693} * 2.303$

$\bigstar\;\; \rm {t = 333.3\;yeaars}$

$\implies \boxed{\rm 333.3 \;years}$