# Calculate a K-Ar Date for a Sample of Biotite

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

**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.