Question

Uranium ares on the earth at the present time typically have a compositing of 99.3% of the isotope ₉₂U²³⁸ and 0.7% of the isotope ₉₂U²³⁵. The half lives of these isotopes are 4.47 x 10⁹ y and 7.04 x 10⁸ y respectively. If these isotopes were equally abundant when the earth was formed, estimate the age of the earth.

Answer 1

Let N₀ be number of atoms of each isotope at the time of formation of the earth (t = 0) and N₁ and N₂ the number of atoms at present (t = t). Then

Further it is given that

Equating (iii) and (iv) and taking log both sides, we have

Substituting the values, we have