Problem 102P

A radiometric dating technique uses the decay of U-238 to Pb-206 (the half-life for this process is 4.5 billion years) to determine the age of the oldest rocks on Earth and by implication the age of Earth itself. The oldest uranium- containing rocks on Earth contain approximately equal numbers of uranium atoms and lead atoms. Assuming the rocks were pure uranium when they were formed, how old are the rocks?

Solution 102P:

Here, we are going to determine the age of the rocks.

Step1:

The time taken for one-half of a sample to disappear is called its half life(t1/2). The half life period for the process is 4.5 x 109 years

Now, we know that,

t1/2 =

k =

=

= 0.462 x 10-9 yr-1

Step2:

Again, from kinetics we have,

t = ln (1 +)

Where t = age of the rock

D = number of atoms of daughter product today

P = number of atoms of the parent isotope today

k = decay constant

Since the number of uranium and lead atoms are equal, therefore, D = P.

Substituting the values in the above expression, we get,

t = ln (1 +)

t = ln (1 +)

t = ln 2

t =

t = 1.5 x 109 yrs

Thus, the rock is 1.5 billion years old.

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