Question

If a substance with half-life $3$ days is taken at other place in $12$ days, what amount of substance is left now ?

• A. 44565
• B. 44569
• C. 44577
• D. Jan-32

Answer 1

Answer: (C)

44577

Answer 2

The time in which mass of a radioactive substance remains half of its initial mass is known as its half life $\left(t_{1 / 2}\right)$. $t_{1 / 2}=\frac{0.693}{\lambda}$ (disintegration constant) Half-life is independent of temperature, pressure and number of atoms present initially. $T_{1 / 2}$ of a non radioactive substance is infinity Half-life $t_{1 / 2}=3$ days Total time $=12$ days $N=N_{0}\left(\frac{1}{2}\right)^{n}$ where $N_{0}=$ Initial amount $N=$ Amount left after disintegration $n=\frac{\text { Total time }}{\text { Half-life }}$ $n=$ number of half life $=\frac{12}{3} =4$ $N =\left(\frac{1}{2}\right)^{4}$ $=\frac{1}{16}$