Answer: The sample must have passed 4 half-lives after the sample was originally formed.
Explanation: This is a type of radioactive decay and all the radioactive process follow first order kinetics.
Equation for the reaction of decay of radioisotope follows:
To calculate the initial amount of , we will require the stoichiometry of the reaction and the moles of the reactant and product.
Expression for calculating the moles is given by:
Moles of left =
Moles of
By the stoichiometry of above reaction,
1 mole of is produced by 1 mole
So, 0.7429 moles of will be produced by =
Amount of decomposed will be = 0.7429 moles
Initial amount of will be = Amount decomposed + Amount left = (0.0495 + 0.7429)moles = 0.7924 moles
Now, to calculate the number of half lives, we use the formula:
where,
a = amount of reactant left after n-half lives = 0.0495 moles
= Initial amount of the reactant = 0.7924 moles
n = number of half lives
Putting values in above equation, we get:
Taking log on both sides, we get