The half life of a radioactive element is 140 days. After 560 days, one gram of the element will be reduced to:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 0.0625 g
Radioactive decay is a first order process, so its half-life does not depend on the amount present: in every half-life, half of what is left decays. After n half-lives the amount left is:
\( \displaystyle N = N_0\left(\frac{1}{2}\right)^{n} \)
The number of half-lives in 560 days:
\( \displaystyle n = \frac{560\ \text{days}}{140\ \text{days}} = 4 \)
\( \displaystyle N = 1\ \mathrm{g} \times \left(\frac{1}{2}\right)^{4} = \frac{1}{16}\ \mathrm{g} = 0.0625\ \mathrm{g} \)
Step by step: 1 g → 0.5 g → 0.25 g → 0.125 g → 0.0625 g. So one gram is reduced to 0.0625 g.