A radioactive substance decays to ((1)/(16)) ^ th of its initial...

A radioactive substance decays to

{\left(\dfrac{1}{16}\right)}^{\text{th}}

of its initial activity in

80

days. The half life of the radioactive substance expressed in days is ________.

Correct answer

Step-by-step solution

${N}_{0}\overset{t\dfrac{1}{2}}{⟶}\dfrac{{N}_{0}}{2}\overset{t\dfrac{1}{2}}{⟶}\dfrac{{N}_{0}}{4}\overset{t\dfrac{1}{2}}{⟶}\dfrac{{N}_{0}}{8}\overset{t\dfrac{1}{2}}{⟶}\dfrac{{N}_{0}}{16}$

$4 \times t\dfrac{1}{2} = 80$

$t\dfrac{1}{2} = 20$ days

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