Question

In an ore containing uranium, the ratio of U²38 to Pb²06 is 3. Calculate the age of the ore, assuming that all the lead present in the ore is the final stable product of U²38. Take the half-life of U²38 to be 4.5 × 10⁹ yr.

• A. \(1.6 \times 10^9\,\text{yr}\)
• B. \(1.5 \times 10^4\,\text{yr}\)
• C. \(1.867 \times 10^9\,\text{yr}\)
• D. 2 × 10⁵yr

Hint:

In radioactive dating, always express present and decayed nuclei correctly before applying decay law.

Answer 1

The Correct Option is C

Step 1: Let initial number of uranium nuclei be N₀. Present uranium nuclei N = 3, lead nuclei =1. (N)/(N₀ - N) = 3 ⟹ N₀ = 4
Step 2: Radioactive decay law: (N)/(N₀) = ((1)/(2))ᵗ/T_¹/² (3)/(4) = ((1)/(2))ᵗ/⁴.⁵ᵗⁱᵐᵉˢ¹⁰^⁹
Step 3: Solving, t = 1.867 × 10⁹yr