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 ____________.
Answer (integer)
20
Solution
<p>$N = {N_0}{e^{ - \lambda t}}$</p>
<p>$\Rightarrow {{6.25} \over {100}} = {e^{ - \lambda t}}$</p>
<p>$$ \Rightarrow {e^{ - \lambda t}} = {1 \over {16}} = {\left( {{1 \over 2}} \right)^4}$$</p>
<p>$\Rightarrow t = 4{t_{1/2}}$</p>
<p>$\Rightarrow t = 20$ years</p>
About this question
Subject: Physics · Chapter: Atoms and Nuclei · Topic: Radioactivity
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