Answer: Thus the fraction decayed is [tex]\frac{7a_o}{8}[/tex]
Explanation: Radioactive decay follow first order kinetics.
Now, to calculate the amount decayed after n half lives, we use the formula:
[tex]a=\frac{a_o}{2^n}[/tex]
where,
a = amount of reactant left after n-half lives
[tex]a_o[/tex] = Initial amount of the reactant
n = number of half lives = 3
Putting values in above equation, we get:
[tex]a=\frac{a_0}{2^3}[/tex]
[tex]a=\frac{a_0}{8}[/tex]
The fraction decayed after 3 half lives will be [tex]\frac{1}{8}[/tex] of the initial amount.
Thus the fraction decayed is [tex]a_0-\frac{a_0}{8}=\frac{7a_o}{8}[/tex]
