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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