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 . If one plots (A₁₁₀/A_ 0,110 ) versus time for ¹¹⁰ Ag for the first 50 s , what is the expected shape of the plot? Time (s) Activity A ( 10⁸ disintegrations s ⁻¹ ) Time (s) Activity A ( 10⁸ disintegrations s ⁻¹ ) 20 11.799 200 3.0828

Step-by-step solution

The activity of a single radioactive isotope follows the exponential decay law: A₁₁₀ = A_ 0,110 e^ - ₁₁₀ t where A₁₁₀ is the activity at time t , A_ 0,110 is the initial activity, and ₁₁₀ is the decay constant of ¹¹⁰ Ag . Dividing by A_ 0,110 and taking the natural logarithm on both sides, we get: ( A₁₁₀ A_ 0,110 ) = - ₁₁₀ t This equation represents a linear relationship of the form y = mx , where the y-axis is ( A₁₁₀ A_ 0,110 ) and the x-axis is time t . The slope of this line is m = - ₁₁₀ . Since the decay consta