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.

Given: 10 milligrams of sample decays to 5 milligrams in 23 days.

Mayme

Skilled2021-09-10Added 103 answers

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$N=1\text{}\in \text{}N={N}_{0}{e}^{-kt}$

$1=10{e}^{-0.03t}$

$t=\frac{\mathrm{ln}10}{0.03}=76.4$ 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.

Radio-active decay of a sample is given by

Where,

Calculation:

At

At

Substitute in

To calculate the number of days to decay the sample to 1 milligram, Substitute

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.