Question

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?

Answer 1

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

                                $N =$ N₀ $(\frac{1}{2} )^\frac{t}{T}$

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;

                $1.0 = 4.0 (\frac{1}{2} )^\frac{t}{1620}$

                $log \frac{1.0}{4.0} = \frac{1}{1620} log \frac{1}{2}$

                $log 0.25 = \frac{t}{1620} log 0.5$

                $-0.60 = \frac{t}{1620} (-0.301)$

                  $t = \frac{972}{0.301}$

                  $t= 3229.2 sec$

Therefore, the time elapsed is 3229.2 days

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