How long will it take for a 750 mg sample of radium with a half life of 15 days to decay to exactly 68mg?

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52 da  

Step-by-step explanation:

Whenever a question asks you, "How long to reach a certain concentration?" or something similar, you must use the appropriate integrated rate law expression.

The integrated rate law for a first-order reaction is  

ln([A₀]/[A] ) = kt

Data:

[A]₀ = 750 mg

 [A] =    68 mg

t_ ½ =   15 da

Step 1. Calculate the value of the rate constant.

 t_½ = ln2/k     Multiply each side by k

kt_½ = ln2         Divide each side by t_½

      k = ln2/t_½

         = ln2/15

         = 0.0462 da⁻¹

Step 2. Calculate the time

ln(750/68) = 0.0462t

         ln11.0 = 0.0462t

            2.40 = 0.0462t     Divide each side by 0.0462

                   t = 52 da