The time taken for 80 g of uranium (t1/2 = 4.5 × 109 years) to decay to 10 g would be -

Foundation

Chemistry Foundation

Nuclear Chemistry

Question

The time taken for 80 g of uranium (t_1/2 = 4.5 × 10⁹ years) to decay to 10 g would be -

9.0 × 10⁹ years

4.5 × 10⁹ years

13.5 × 10⁹ years

18.0 × 10⁹ years

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$N_{1} = N_{0} {(\frac{1}{2})}^{n} \Rightarrow 10 = 80 {(\frac{1}{2})}^{n}$
   where, n = number of t_1/2
$\Rightarrow \frac{10}{80} = {(\frac{1}{2})}^{n} \Rightarrow {(\frac{1}{2})}^{3} = {(\frac{1}{2})}^{n}$
n = 3
so the time taken = 3 × 4.5 × 10⁹ years
               = 13.5 × 10⁹ years