Explanation:
Expression for rate constant and half-life is as follows.
k = [tex]\frac{1}{t} ln(\frac{a}{a - x})[/tex]
The given data is as follows.
a = 8540 disintegrations/min
and, (a - x) = 6990 disintegrations/min
Putting the given values into the above formula as follows.
k = [tex]\frac{1}{10} \times ln(\frac{8540}{6990})[/tex]
= 0.02 [tex]day^{-1}[/tex]
Now, we will calculate the half-life as follows.
Half-life = [tex]\frac{ln 2}{k}[/tex]
= 34.6 days
Thus, we can conclude that the half-life of 37Ar in days is 34.6 days.
