Answer : The half life of the radioisotope is 2.7 hours.
Explanation :
Radioactive disintegration is a first order reaction. The disintegration equation can be written as,
Here N is the amount of radioactive substance left = 8 counts
No is the initial amount of Radioactive substance = 64 counts
t is the time = 8 hours
λ is the disintegration constant
Let us rearrange the equation to solve for λ
Take natural logarithm "ln" on both sides
Divide both sides by t
Let us plug in the given values.
The disintegration constant, λ is 0.26.
λ and half life ( t1/2) are related to each other by following equation.
Let us plug in the value of λ
The half life of the radioisotope is 2.7 hours.