First slide

Radio activity

Question

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

Easy

A

75 hrs
B

65 hrs
C

55 hrs
D

45 hrs

Solution

Undecayed isotope $= 1 - \frac{7}{8} = \frac{1}{8}$
$∴ \frac{N}{N_{0}} = {(\frac{1}{2})}^{t / T} \Rightarrow (\frac{1}{8}) = {(\frac{1}{2})}^{t / 15} \Rightarrow \frac{t}{15} = 3 or t = 45 hours .$

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