The contents of a rock have a 206Pb to 238U mass ratio of 0.135:1.00. Assuming that the rock did not contain any 206Pb at the time of its formation, determine the age of the rock. Uranium-238 decays to lead-206 with a half-life of 4.5 billion years. Express the time to two significant digits.

The age of the rock is

Explanation:

The equation used to calculate rate constant from given half life for first order kinetics:

where,

= half life of the reaction = 4.5 billion years =    

Putting values in above equation, we get:

We are given:

Mass ratio of 206-Pb to 238-U = 0.135 : 1.00

Rate law expression for first order kinetics is given by the equation:

where,

k = rate constant  =

t = time taken for decay process = ? yr

= initial amount of the sample = [1.00 + 0.135] = 1.135 g

[A] = amount left after decay process = 1.00 grams

Putting values in above equation, we get:

Hence, the age of the rock is