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More Ways to Use This Stuff

Let's try something a little more complicated...

You are observing a mystery radioactive isotope.  At 4 pm, there are 2.5 grams and at 9 pm, there are 1.7 grams.  What's the half-life?

We'll have to solve for h this time!

A = A not * 2^( -t / h ) ... 1.7 = 2.5 * 2^( -5 / h ) ... clear the path! ... ( 1.7 / 2.5 ) = 2^( -5 / h ) ... How can we get that h down? ... Ln( 1.7 / 2.5 ) = Ln( 2^( -5 / h ) ) ... Ln( 1.7 / 2.5 ) = ( -5 / h ) * Ln( 2 ) ... OK, we just have to do some more algebra... h * Ln( 1.7 / 2.5 ) = -5 Ln( 2 ) ... multiply by h... ... h = -5 Ln(2 ) / Ln( 1.7 / 2.5 ) = approximately 8.97 hours

The half-life is about 8.97 hrs.

 

TRY IT:

Doing some digging on an alien planet, you find the bones of a Carbon-based alien life form.  If a live alien specimen has 0.7 mg of Carbon-14 in it's bones and you measure 0.2 mg, how old is the specimen?