Amoon rock collected by a u. s. apollo mission is estimated to be 4.20 billion years old by uranium/lead dating. assuming that the rock did not contain any lead when it was formed, what is the current mass of 206pb per 1.305 g of 238u in the rock? the half-life of 238u is t1/2 = 4.47 × 109 years.

Answer : The current mass of 206-Pb per 1.305 g of 238-U in the rock is, 0.54 grams.

Explanation :

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

To calculate the rate constant, we use the formula :

Now we have to calculate the moles of 238-U.

Now we have to calculate the amount left.

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

where,

k = rate constant

t = time taken for decay process

a = initial amount or moles of the reactant

a - x = amount or moles left after decay process

Putting values in above equation, we get:

Now we have to calculate the decomposed moles of uranium.

As we know that,

1 mole of is produced by 1 mole

The decomposed moles of Pb =

Now we have to calculate the current mass of 206-Pb per 1.305 g of 238-U in the rock.

Therefore, the current mass of 206-Pb per 1.305 g of 238-U in the rock is, 0.54 grams.