How can we calculate a K-Ar date for a sample of biotite from a gneiss containing certain percentages of 40K and 40Ar, along with decay constants and atomic weights?
Calculating a K-Ar Date for a Sample of Biotite
To calculate a K-Ar date for a sample of biotite, we need to utilize the provided information regarding the composition of the sample and the decay constants involved in K-Ar dating. The key components required for this calculation include the percentage of K2O, the amount of 40Ar, the atomic abundances, and the decay constants.
Initial Steps:
Firstly, we need to determine the amount of 40K and 40Ar in the sample based on the given data. The sample of biotite from the gneiss contains 9.00% K2O and 2.424 ug/g of 40Ar.
Calculating Amount of Potassium (K):
- The atomic weight of K is 39.098.
- Convert the percentage of K2O to the amount of K in the sample: (9.00% * K2O) * (39.098 / 100).
Calculating Amount of 40K:
- Multiply the amount of K by the atomic abundance of 40K (0.01167%): amount of K * (0.01167 / 100).
Utilizing Decay Constants:
The decay constants provided in the question (he = 0.581 x10^-10, 2 = 5.543 x10^-10) are crucial for the calculation.
Calculation:
To calculate the age of the sample, we use the formula: age = (1 / (2 * decay constant)) * ln(1 + (amount of 40K / amount of 40Ar)).
Now, by substituting the values obtained into the formula, we can determine the K-Ar date for the sample of biotite from the gneiss.