🤓 Based on our data, we think this question is relevant for Professor Bindell's class at UCF.

Step 1:

$\overline{){{\mathbf{t}}}_{\raisebox{1ex}{$\mathbf{1}$}\!\left/ \!\raisebox{-1ex}{$\mathbf{2}$}\right.}{\mathbf{}}{\mathbf{=}}\frac{\mathbf{ln}\mathbf{}\mathbf{2}}{\mathbf{k}}}\phantom{\rule{0ex}{0ex}}\mathbf{}\mathbf{k}\mathbf{=}\frac{\mathbf{ln}\mathbf{}\mathbf{2}}{{\mathbf{t}}_{\raisebox{1ex}{$\mathbf{1}$}\!\left/ \!\raisebox{-1ex}{$\mathbf{2}$}\right.}}\phantom{\rule{0ex}{0ex}}\mathbf{k}\mathbf{}\mathbf{=}\frac{\mathbf{0}\mathbf{.}\mathbf{693}\mathbf{}}{\mathbf{1}\mathbf{.}\mathbf{27}\mathbf{\times}{\mathbf{10}}^{\mathbf{9}}\mathbf{}\mathbf{yr}}$

**k = 5.4579x10 ^{-10} yr^{-1}**

Step 2:

$\overline{){\mathbf{ln}}{\mathbf{}}{\mathbf{\left[}\mathbf{A}\mathbf{\right]}}_{{\mathbf{t}}}{\mathbf{}}{\mathbf{=}}{\mathbf{}}{\mathbf{-}}{\mathbf{kt}}{\mathbf{}}{\mathbf{+}}{\mathbf{}}{\mathbf{ln}}{\mathbf{\left[}\mathbf{A}\mathbf{\right]}}_{{\mathbf{0}}}}\phantom{\rule{0ex}{0ex}}\mathbf{ln}\mathbf{}\frac{{\mathbf{\left[}\mathbf{A}\mathbf{\right]}}_{\mathbf{t}}}{{\mathbf{\left[}\mathbf{A}\mathbf{\right]}}_{\mathbf{0}}}\mathbf{}\mathbf{=}\mathbf{}\mathbf{-}\mathbf{kt}$

Potassium-40 decays to argon-40 with a half-life of 1.27 x 10^{9} yr.

You may want to reference (Pages 913 - 916)Section 21.4 while completing this problem.

What is the age of a rock in which the mass ratio of ^{40}Ar to ^{40}K is 4.2?

Frequently Asked Questions

What scientific concept do you need to know in order to solve this problem?

Our tutors have indicated that to solve this problem you will need to apply the First Order Half Life concept. You can view video lessons to learn First Order Half Life. Or if you need more First Order Half Life practice, you can also practice First Order Half Life practice problems.

What professor is this problem relevant for?

Based on our data, we think this problem is relevant for Professor Bindell's class at UCF.