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Finding the Decay constant(λ):
λ = 0.693 / (half-life)
we are given that the half-life is 36 hours
λ = 0.693 / (36)
λ = 0.01925 /hour
Time taken for 87% decay:
Since decay is first-order, we will use the formula:
[tex]t = \frac{2.303}{decay constant}log(\frac{A_0}{A} )[/tex]
Where A₀ is the initial amount and A is the final amount
Let the initial amount be 100 mg,
the final amount will be 87% of 100
Final amount = 100*87/100 = 87 mg
Replacing the values in the equation:
[tex]t = \frac{2.303}{0.01925}log(\frac{100}{87} )[/tex]
[tex]t = \frac{2.303}{0.01925}*0.06[/tex]
t = 7.18 hours
We used 'hours' as the unit because the unit of the decay constant is '/hour'
Therefore, the drug will decay to 87% of initial dosage after 7.18 hours