How Do You Calculate Earth's Age Using Half-Life Decay Law?

[IceZero]

Well, hi guys, I know I am new to this forum and all but I am having a mental block with one of my physics questions. My teacher gave me this "mind-buster" question, and I want to solve it. Can give me some help or hints on how to go about solving it. I don't need the answer to it, i just need hits or explanations.

Problem: To solve this problem you should remember the general decay law from high school calculus. The radioactive decat of nuclei is usually described quantitatively with the parameter T. Let us define the half-life ,T, as the time in which 1/2 of the particles decay. The natural uranium ore now consists of ç1=99.28% 238U and ç2=0.72% 235U. Half-life periods of 238U and 235U nuclei are correspondingly equal to T1=4.47*10^9 years and T2=0.70*10^9 years. Estimate the Earth's age assuming the amounts of two isotopes were equal at the moment of birth of our planet.

 

[lavalamp]

If the initial number of atoms for each isotope is the same (which I think is what you're getting at), then:

since No = N/(e^-[lamb]t)

ln No = Ln N - [lamb]t

therefore ln N - [lamb]t (for U-235) = ln N - [lamb]t (for U-238)

Also, you have been told that:

100 * N(238)  = 99.28
-------------
N(235)+N(238)

And:

100 * N(235)  = 0.72
-------------
N(235)+N(238)

All of which means that with various re-arrangements and substitutions you should be able to find your answer.