A rock is 1.5 × 10⁹ years old. Uranium decays to lead with half-life 4.5 × 10⁹ years. Assuming no lead initially, find the present Pb/U ratio. Given 2¹ᐟ³ = 1.259.
Physics · Nuclear physics
JEE Mains Advanced

Question

A rock is 1.5 × 10⁹ years old. Uranium decays to lead with half-life 4.5 × 10⁹ years. Assuming no lead initially, find the present Pb/U ratio. Given 2¹ᐟ³ = 1.259.

G1 Physics · Accepted Answer

After t/T½ = 1/3, the remaining uranium fraction is 2⁻¹ᐟ³=1/1.259≈0.794. Lead formed fraction ≈0.206, so Pb/U≈0.206/0.794≈0.259.