A sample of radioactive nuclei has a half life of 5.5 years. The fraction of sample remaining undecayed after 22 years is
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 6.25%
Given:
Half-life, $T_{1/2} = 5.5\,\text{years}$
Total time, $t = 22\,\text{years}$
Fraction of undecayed nuclei:
$\frac{N}{N_0} = \left(\frac{1}{2}\right)^{t/T_{1/2}}$
Substitute values:
$\frac{N}{N_0} = \left(\frac{1}{2}\right)^{22/5.5} = \left(\frac{1}{2}\right)^4 = \frac{1}{16}$ = 6.25%
Final Answer: $\frac{N}{N_0} = \frac{1}{16}$ = 6.25%