The age of a rock can be estimated by measuring the amount of 40Ar trapped inside. The calculation is based on the fact that 40K decays to 40Ar by a first-order process. It also assumes that none of the 40Ar produced by the reaction has escaped from the rock since it was formed.

40K + e- -> 40Ar k = 5.81 X 10^-11 year^-1

Calculate the half-life of the radioactive decay.

k=0.693/t(1/2). Solve for t(1/2)

What order do you think this is?

From there use that information and find the half life equation.
Then just plug it in to get the answer

Hope that helps!

To calculate the half-life of a radioactive decay process, we can use the decay constant (k) for the process. The decay constant is defined as the probability that a nucleus will decay per unit time.

In this case, the decay process is:

40K -> 40Ar

Given that the decay constant for this process is k = 5.81 X 10^-11 year^-1, we can use the following equation to calculate the half-life (t½):

t½ = ln(2) / k

Where ln is the natural logarithm and 2 is the factor by which the original quantity is reduced during one half-life.

Plugging in the value of k:

t½ = ln(2) / (5.81 X 10^-11 year^-1)

Using a calculator to perform the calculation:

t½ ≈ 1.19 X 10^10 years

Therefore, the half-life of the radioactive decay process of 40K to 40Ar is approximately 1.19 X 10^10 years.