A sample contains a mixture of ¹¹⁰ Ag and ¹⁰⁸ Ag isotopes, each having an initial activity of 8.0 10⁸ disintegrations per second. ¹⁰⁸ Ag is known to have a larger half-life than ¹¹⁰ Ag , specifically 144 s . Calculate the activity corresponding to ¹¹⁰ Ag at t = 50 s . Time (s) Activity A ( 10⁸ disintegrations s ⁻¹ ) Time (s) Activity A ( 10⁸ disintegrations s ⁻¹ ) 20 11.799 200 3.0828 40 9.1680 300 1.8899 60 7.4492 4

Step-by-step solution

The total activity of the sample at any time t is the sum of the activities of the two isotopes: A(t) = A₁₁₀(t) + A₁₀₈(t) For ¹⁰⁸ Ag , the initial activity is A₁₀₈(0) = 8.0 10^8 disintegrations s ⁻¹ and its half-life is T_ 1/2 = 144 s . The activity of ¹⁰⁸ Ag at t = 100 s is: A₁₀₈(100) = 8.0 10^8 e^ - 100 2 144 = 8.0 10^8 e^ -0.4813 4.943 10^8 disintegrations s ⁻¹ From the given table, the total activity at t = 100 s is A(100) = 5.4115 10^8 disintegrations s ⁻¹ . Thus, the activity of ¹¹⁰ Ag at t = 100 s is: A₁₁₀(1