Asample contains 10.5 g of the radioisotope pb-212 and 157.5 g of its daughter isotope, bi-212. how many half-lives have passed since the sample originally formed?
4
14
15
147.5

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