A sample of radioactive nuclei has a half life of 5.5 years. The fraction of sample remaining undecayed after 22 years is

6.25%

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%