Question

If the Rb-Sr isochron formed by a suite of gabbro samples has a slope of 0.0265, then the calculated age of the gabbro in million years is_____. (in integer).
[Use λ(⁸⁷Rb) = 1.42 x 10^-11 year^-1]

Hint:

In Rb-Sr dating, the slope of the isochron equals \((e^{\lambda t}-1)\). Always apply logarithm after adding 1 to slope.

Answer 1

Correct Answer: 1840

Step 1: Recall the relation.
For Rb-Sr dating, the slope of the isochron \(m\) is: \[ m = e^{\lambda t} - 1 \] where \(\lambda\) is the decay constant and \(t\) is the age. Step 2: Substitute known values.
\(\lambda = 1.42 \times 10^{-11}\ \text{year}^{-1}, \quad m = 0.0265.\) So, \[ 0.0265 = e^{\lambda t} - 1 \quad \Rightarrow \quad e^{\lambda t} = 1.0265 \] Step 3: Take natural log.
\[ \lambda t = \ln(1.0265) \] \[ \ln(1.0265) \approx 0.02615 \] Step 4: Solve for \(t\).
\[ t = \frac{0.02615}{1.42 \times 10^{-11}} \] \[ t \approx 1.8415 \times 10^{9}\ \text{years} \] \[ t \approx 1841\ \text{million years} \] Rounding to integer: \[ \boxed{1840\ \text{million years}} \]