Respuesta :
The original mass of the Argon-37 sample (N₀) was 14.98651g or approximately 15g. We Use the equation for first-order kinetics for determining the original mass of the given Argon-37 sample.
What is first order rate equation?
If the rate of radioactive decay is first order, we can write r = k[N]1, where N is the quantity of radioisotope present at the time the rate is recorded, k is the isotope's first order rate constant, and r is the rate of decay as observed.
According to First-Order Rate Equation,
[tex]ln(\frac{N}{N_{0} } )=-kt[/tex]
Here,
N = The amount of radioisotope left after "t" time.
N₀= The initial amount of radioisotope,
k = Rate constant of the radioisotope.
t = Time
Given,
N = 2. 14 g.
N₀ = ?
k = 0. 0198
t = 98. 3 days
Now, substituting these values in the first order rate equation we get,
[tex]ln(\frac{N}{N_{0} } )=-kt\\ln(\frac{2.14}{N_{0} } )=-0.0198*98.3\\ln(\frac{2,14}{N_{0} } )=-1.94634\\\frac{2.14}{N_{0} } =e^{-1.94634} \\\frac{2.14}{N_{0} }=0.142795\\N_{0} = 14.98651g[/tex]
Hence, the original mass of the sample (N₀) was 14.98651 g or approximately 15 g.
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