Question

After $150$ days, the activity of a radioactive sample is $5000$ dps. The activity becomes $2500$ dps after another $75$ days. The initial activity of the sample is

• A. $20000$ dps
• B. $40000$ dps
• C. $7500$ dps
• D. $10000$ dps

Answer 1

Answer: (A)

$20000$ dps

Let the initial activity be $R_o$ dps.

Using 1st order decay equation, $\lambda t=2.303lo{g}_{10}\frac{R_o}{R}$

Given: After time $t=150days$, activity becomes $R=5000$ dps

After time $t=150+75=225days$, activity becomes $R=2500$ dps

$⟹\lambda \left(150\right)=2.303lo{g}_{10}\frac{R_o}{5000}$ ..............(1)

And, $\lambda \left(225\right)=2.303lo{g}_{10}\frac{R_o}{2500}$ ..............(2)

Dividing (1) from (2), we get:

$\frac{225}{150}=\frac{lo{g}_{10}{R}_o-lo{g}_{10}2500}{lo{g}_{10}{R}_o-lo{g}_{10}5000}$

$\therefore lo{g}_{10}{R}_o=4.3⟹R_o=20000$ dps