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

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

Tardigrade Admin · Accepted Answer

Activity of sample becomes 2500 from 5000 in 75 days therefore its half life is 75 days, so R =( R 0/2(150)75)=5000 ⇒ R 0=5000 × 4=20,000

Q. 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

20000 dps

40000 dps

7500 dps

10000 dps

Activity of sample becomes $2500$ from $5000$ in $75$ days therefore its half life is $75$ days, so
$R = \frac{R _{0}}{2 ^{\frac{150}{75}}} = 5000$
$\Rightarrow R_{0} = 5000 \times 4 = 20, 000$

Q. 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