Question

The ⁸⁷Sr/⁸⁶Sr ratio of a 1000 Ma granite was measured as 0.8001. If its ⁸⁷Rb/⁸⁶Sr ratio is 2.499, what was the Sr isotopic ratio of the source at the time of derivation of the granite? (decay constant of ⁸⁷Rb=1.39 × 10^-11 yr^-1)
(Round off to three places of decimals)

Answer 1

Correct Answer: 0.765

To find the initial ⁸⁷Sr/⁸⁶Sr ratio of the source from which the granite was derived, we will use the following formula: 

R_t = R₀ + (e^λt - 1) (⁸⁷Rb/⁸⁶Sr)

Where:

• R_t = Measured ⁸⁷Sr/⁸⁶Sr ratio today = 0.8001
• R₀ = Initial ⁸⁷Sr/⁸⁶Sr ratio we are solving for
• ⁸⁷Rb/⁸⁶Sr = 2.499
• λ = Decay constant for ⁸⁷Rb = 1.39 × 10^-11 yr^-1
• t = 1000 Ma = 1000 × 10⁶ years

Step 1: Calculate e^λt
e^λt = e^{(1.39 × 10-11 yr-1 × 1000 × 106 yr)} = e^0.0139 ≈ 1.0140
Step 2: Substitute known values and solve for R₀
0.8001 = R₀ + (1.0140 - 1) × 2.499
0.8001 = R₀ + 0.0350
R₀ = 0.8001 - 0.0350 = 0.7651

Upon rounding R₀ to three decimal places, we find it to be 0.765.