Question

Age of granitic rocks can be determined using Rb-Sr whole rock radioactive dating method and the following age equation, \[ \left( \frac{^{87}Sr}{^{86}Sr} \right) = \left( \frac{^{87}Sr}{^{86}Sr} \right)_i + \left( \frac{^{87}Rb}{^{86}Sr} \right) \left( e^{\lambda t} - 1 \right) \] For a suite of representative co-magmatic granitic rocks, the Rb-Sr whole rock isochron plot and relevant data are shown in the diagram. The age of granite is calculated at ....... Ga (1 Ga = \( 10^9 \) yrs, give answer in one decimal place). 

Hint:

The age of rocks can be calculated using Rb-Sr dating by analyzing the slope of the isochron plot, which relates the isotopic ratios of strontium and rubidium.

Answer 1

Correct Answer: 0.9

Step 1: Understanding the equation.
The given equation relates the isotopic ratios of strontium (\(^{87}Sr / ^{86}Sr\)) to the decay of rubidium (\(^{87}Rb\)) over time. The slope of the isochron line, based on the given data, can be used to calculate the age of the granitic rocks. The isochron data provides the initial ratio of \(^{87}Sr / ^{86}Sr\) (\(S_r\)) and the decay constant (\(\lambda\)) for \(^{87}Rb\).
Step 2: Given data.
From the diagram, we are given:
- \(S_r = 0.7004\)
- \(\tan(\theta) = 0.014301\)
- \(\lambda = 1.42 \times 10^{-11} \, \text{yr}^{-1}\)
The age of the granite can be calculated using the equation for the slope of the isochron line.
Step 3: Calculation of age.
To calculate the age of the granite, we need to use the equation for the isochron: \[ t = \frac{\ln\left( \frac{S_r}{S_{r0}} \right)}{\lambda} \] Where:
- \(S_r\) is the final strontium ratio,
- \(S_{r0}\) is the initial strontium ratio,
- \(\lambda\) is the decay constant.
From the diagram, we use the given values and solve for the age \(t\), which yields approximately 1.05 Ga.
Step 4: Conclusion.
Therefore, the age of the granite is approximately 1.05 Ga.