Question

The half life of radioactive substance is 4 days. What is the probability of decay of a nucleus in 12 days?

• A. $1/8$
• B. $7/8$
• C. $3/4$
• D. $1/3$

Answer 1

The correct option is B $7/8$

$N=N_0(\frac{1}{2}{)}^n$
We know,
$n=\frac{t}{t_{1/2}}=\frac{12}{4}=3$

$N=N_o(\frac{1}{2}{)}^3=\frac{N_0}{8}$

Sample of survived nuclei $=\frac{N_0}{8}$

Sample of decayed nuclei $=\frac{7N_0}{8}$

Probability $=\frac{\frac{7{\mathrm{N/}}_0}{8}}{{\mathrm{N/}}_0}=\frac{7}{8}$