Calculating the Age of Granite Using Half-lives

What is the age (in billions of years) of the granite (unit P) if 1.25 half-lives of 238U/206Pb have elapsed, and the half life of 238U/206Pb is 4.5 billion years?

The age of the granite (unit P) is 2.83 billion years (approx.)

The age of the granite (unit P) can be calculated using the following formula:

Age = ㏑(Nf/Ni) / λ

where Nf/Ni is the ratio of the number of daughter atoms (206Pb) to parent atoms (238U) in the sample, and λ is the decay constant for 238U, which is equal to In(2) / T1/2, where T1/2 is the half-life of 238U. Given that 1.25 half-lives of 238U/206Pb have elapsed, we know that the ratio of 206Pb to 238U in the sample is:

Nf/Ni = 1/2^(1.25) = 0.237

Substituting this value and the decay constant into the above formula, we get:

Age = In(0.237) / In(2)/4.5 = 2.83

billion years (rounded to two decimal places)

Therefore, the age of the granite (unit P) is approximately 2.83 billion years.

What is the age (in billions of years) of the granite (unit P) if 1.25 half-lives of 238U/206Pb have elapsed, and the half life of 238U/206Pb is 4.5 billion years?

The age of the granite (unit P) is 2.83 billion years (approx.)