Question

A Rb–Sr isochron plot of cogenetic volcanic rocks yielded a slope of 0.003. The eruption age of these rocks is ............... Ma. (Round off to one decimal place)

Hint:

For Rb–Sr dating, use the isochron plot slope to determine the age by dividing the logarithm of the slope by the decay constant \( \lambda^{87}\text{Rb} \).

Answer 1

Step 1: Use the equation for the age of rocks.
The formula for calculating the age of rocks from an isochron plot is: \[ \text{Age} = \frac{\ln(1 + \text{Slope})}{\lambda^{87}\text{Rb}} \] Given that the slope is 0.003, and \( \lambda^{87}\text{Rb} = 1.39 \times 10^{-11} \, \text{yr}^{-1} \): \[ \text{Age} = \frac{\ln(1 + 0.003)}{1.39 \times 10^{-11}} = \frac{\ln(1.003)}{1.39 \times 10^{-11}} \] Step 2: Simplify the calculation.
Using \( \ln(1.003) \approx 0.002995 \): \[ \text{Age} = \frac{0.002995}{1.39 \times 10^{-11}} = 2.16 \times 10^{8} \, \text{years} = 216.0 \, \text{Ma} \] Final Answer: \[ \boxed{216.0} \]