Answer:
It takes 178.4 years to drop the activity from 15.0 Ci to 0.25 Ci
Explanation:
Step 1: Data given
Half-life time = 30.2 years
Initial activity = 15.0 Ci
Final activity = 0.250 Ci
Step 2: Calculate the time needed
N / No = e^(-0.693 * t / T1/2)
⇒ with N = The activity after dropped = 0.250 Ci
⇒ with N0 = the initial activity = 15.0
⇒ with t= the time (in years) needed to drop the activity from 15.0 to 0.250
⇒ with t1/2 = the half- life time is 30.2 years
0.250 / 15.0 = e^(-0.693 * t / 30.2)
ln(0.250/15.0) = (-0.693 * t / 30.2)
-4.09 * 30.2 = -0.693t
-123.65 = -0.693t
t= 178.4 years
It takes 178.4 years to drop the activity from 15.0 Ci to 0.25 Ci
