A radioactive material with half life of 6.25 years undergoes beta decay. How much fraction of material is decayed after 25 years:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 15/16 **
$\text{Given: Half-life } T_{1/2} = 6.25~\text{years},~ t = 25~\text{years}$
$\text{Fraction of undecayed material: } N/N_0 = \left(\frac{1}{2}\right)^{t/T_{1/2}}$
$N/N_0 = \left(\frac{1}{2}\right)^{25/6.25} = \left(\frac{1}{2}\right)^4 = \frac{1}{16}$
$\text{Fraction decayed: } 1 - N/N_0 = 1 - \frac{1}{16} = \frac{15}{16}$
$\text{Answer: Fraction decayed } = \frac{15}{16}$