A radioactive material is reduced to 1/8 of its original amount in 3 days. If of the material is left after 5 days the initial amount of the material is [2023]

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Solution

Q.
A radioactive material is reduced to 1/8 of its original amount in 3 days. If $8 \times 10^{- 3} kg$ of the material is left after 5 days the initial amount of the material is [2023]

1 32 g

2 256 g

3 40 g

4 64 g

Ans.
(2)

$N = N_{0} {(\frac{1}{2})}^{n}$

$\frac{N_{0}}{8} = N_{0} {(\frac{1}{2})}^{n} \Rightarrow n = 3$

$3 half lives = 3 days$

$1 half life = 1 day$

$5 days = 5 half life$

$N = N_{0} {(\frac{1}{2})}^{n}$

$8 \times 10^{- 3} = N_{0} {(\frac{1}{2})}^{5}$

$N_{0} = 256 \times 10^{- 3} kg$

$\Rightarrow N_{0} = 256 g$

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