CMIIh

2021-09-09

Number of days required for a sample to decay from 10 milligrams to 1 milligram.
Given: 10 milligrams of sample decays to 5 milligrams in 23 days.

Mayme

Formula used:
Radio-active decay of a sample is given by $N={N}_{0}{e}^{-kt}$
Where, ${N}_{0}$ is the initial weight of the sample.
Calculation:
At $t=0,N={N}_{0}=10$
At $t=23,N=5$
Substitute in $N={N}_{0}{e}^{-kt}$
$5=10{e}^{-k\left(23\right)}$
$k=\frac{\mathrm{ln}2}{23}=0.03$
To calculate the number of days to decay the sample to 1 milligram, Substitute
$1=10{e}^{-0.03t}$
$t=\frac{\mathrm{ln}10}{0.03}=76.4$ days.
Conclusion:
Using the formula of radioactive decay, the number of days can be calculated for a sample to decay from 10 milligrams to 1 milligram.

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