The half life for the radioactive decay of potassium-40 to argon-40 is ×1.26109 years.Suppose nuclear chemical analysis shows that there is 0.255mmol of argon-40 for every 1.000mmol of potassium-40 in a certain sample of rock. Calculate the age of the rock.Round your answer to 2 significant digits.

To calculate the age of the rock, we will use the formula for radioactive decay, which is:

N = N0 * (1/2)^(t/T)

where: N is the final quantity of the substance N0 is the initial quantity of the substance t is the time that has passed T is the half-life of the substance

In this case, we know that the ratio of argon-40 to potassium-40 is 0.255mmol to 1.000mmol. This means that 0.745mmol of potassium-40 has decayed into argon-40.

So, we can set up the equation as follows:

0.255 = 1.000 * (1/2)^(t/1.26109)

To solve for t, we first divide both sides by 1.000:

0.255 = (1/2)^(t/1.26109)

Then, we take the natural logarithm of both sides:

ln(0.255) = ln((1/2)^(t/1.26109))

Using the property of logarithms that allows us to bring down exponents, we get:

ln(0.255) = (t/1.26109) * ln(1/2)

Finally, we solve for t:

t = 1.26109 * ln(0.255) / ln(1/2)

Calculating the right side of the equation gives us the age of the rock in years.

Please note that the natural logarithm (ln) is the logarithm to the base e, where e is an irrational and transcendental number approximately equal to 2.718281828459.

Also, please note that the half-life given in the problem is in years, so the age of the rock will also be in years.

Finally, round your answer to 2 significant digits as requested.