A sample containing radioactive ¹³¹ I with a half-life of 8.0 days has an initial activity of 20 Ci at t = 0 . Determine the activity of the sample at t = 4.0 days .

Step-by-step solution

The activity of a radioactive sample at time t is given by the formula: A(t) = A₀ ( 1 2 )^ t T_ 1/2 Given A₀ = 20 Ci , T_ 1/2 = 8.0 days , and t = 4.0 days . Substituting the values: A(4.0) = 20 ( 1 2 )^ 4.0 8.0 A(4.0) = 20 ( 1 2 )^ 1 2 A(4.0) = 20 2 A(4.0) = 10 2 10 1.414 = 14.14 Ci The closest value is 14 Ci .