Question

$2g$ of a radioactive sample having half-life of $15$ days was synthesised on $1^{st}$ $Jan2009$. The amount of the sample left behind on $1^{st}March,$ $2009$ (including both the days) is :

• A. $0g$
• B. $0.125g$
• C. $1g$
• D. $0.5g$

Answer 1

Answer: (B)

$0.125g$

Radioactive sample left is

$N=N_0{\left(\frac{1}{2}\right)}^n$

$N_0$ is initial mass $=2g$

$N$ is mass left behind during radiactivity after time t

$t_{1/2}=15$ days

$t=60$ days

$n$ is time in no. of half life $\frac{60}{15}=4$

Now,

$N=2{\left(\frac{1}{2}\right)}^4=\frac{1}{8}=0.125g$