Question

The half life of the isotope $11Na^{24}$is 15 hrs. How much time does it take for $\frac{7}{8}th$ of a sample of this isotope to decay.

• A. 75 hrs
• B. 65 hrs
• C. 55 hrs
• D. 45 hrs

Answer 1

Answer: (D)

45 hrs

Answer 2

Undecayed isotope $= \frac{3.2 \times 10^{6}}{200 \times 10^{6} \times 1.6 \times 10^{- 19}} = 1 \times 10^{17}$

$\therefore\frac{N}{N_{0}} = \left( \frac{1}{2} \right)^{t/T} \Rightarrow \left( \frac{1}{8} \right) = \left( \frac{1}{2} \right)^{t/15} \Rightarrow \frac{t}{15} = 3$

or t = 45 hours.