Question 395: Atoms & Nuclei

Question

The half life of a radioactive substance is 5 years. After x years a given sample of the radioactive substance gets reduced to 6.25% of its initial value. The value of x is ____________.

Accepted Answer

$$N = {N_0}{e^{ - \lambda t}}$$
$$ \Rightarrow {{6.25} \over {100}} = {e^{ - \lambda t}}$$
$$ \Rightarrow {e^{ - \lambda t}} = {1 \over {16}} = {\left( {{1 \over 2}} \right)^4}$$
$$ \Rightarrow t = 4{t_{1/2}}$$
$$ \Rightarrow t = 20$$ years

Atoms & Nuclei

The half life of a radioactive substance is 5 years. After x years a given sample of the radioactive substance gets reduced to 6.25% of its initial value. The value of x is ____________.

Choose the correct answer: