a sample contains 16.75 g of the radioisotope u-236 and 50.25 g of its daughter isotope, th-232. how long did it take for decay to take place if one half-life of u-236 is 23 million years?
46 million years
92 million years
115 million years

The correct answer is 46 million years.

Explanation: This is a type of radioactive decay and all radioactive decays follow first order kinetics.

Equation for the radioactive decay of is:

We are given half life of , which is 23 million years.

To calculate the rate constant, we use the formula:

Now, to calculate the initial amount of , we use the stoichiometry of the reaction and moles of the reactant and product.

Moles can be calculated by using the formula:

Moles of

Moles of

By stoichiometry of the reaction,

1 mole of is produced by 1 mole

So, 0.2165 moles of will be produced by 0.2165 moles of

Amount of decomposed will be =

Initial amount of will be = Amount decomposed + Amount left = (51.094 + 16.75)g = 68.544g

Expression for rate law for first order kinetics is given by:

where,

k = rate constant

t = time taken for decay process

a = initial amount of the reactant

a - x = amount left after decay process

Putting values in above equation, we get: