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A 4. 0 g sample of ra-226 decays to 1. 0 g. if the half-life of ra-226 is 1620 years, how much time has elapsed?

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Tushargupta0691idn

The time elapsed is 3229.2 days.

First-order reactions include those in radioactive decay. The reduction in radioactive nuclei per unit of time is the rate of decay, or activity, of a sample of a radioactive substance.

The Radioactive Formula is given by

                                [tex]N =[/tex] N₀ [tex](\frac{1}{2} )^\frac{t}{T}[/tex]

Where N₀ = The initial quantity of the substance.

           N = The quantity remained.

           T = the half-life of the decaying quantity.

           t = time elapsed

The initial quantity of the substance = 4.0 g

The quantity remained = 1.0 g

The half-life of the decaying quantity = 1620 years

Using formula;

                [tex]1.0 = 4.0 (\frac{1}{2} )^\frac{t}{1620} \\[/tex]

                [tex]log \frac{1.0}{4.0} = \frac{1}{1620} log \frac{1}{2}\\[/tex]

                [tex]log 0.25 = \frac{t}{1620} log 0.5\\[/tex]

                [tex]-0.60 = \frac{t}{1620} (-0.301)\\[/tex]

                  [tex]t = \frac{972}{0.301} \\[/tex]

                  [tex]t= 3229.2 sec[/tex]

Therefore, the time elapsed is 3229.2 days

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