Question

If $N$${}_0$ is the original mass of the substance of half life period t${}_{1/2}=$$5$ years, then the amount of substance left after $15$ years is:

• A. $N_0/8$
• B. $N_0/16$
• C. $N_0/2$
• D. $N_0/4$

Answer 1

Answer: (A)

$N_0/8$

Amount left after decay is given by N

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

$n=$ number of half lives$=\frac{t}{t_{1/2}}=\frac{15}{5}=3$

$\therefore$Amount left

$=N=N_0{\left(1/2\right)}^3$

$=\frac{N_0}{8}$