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More Ways to Use This Stuff

Let's walk through a problem without the formula first just to make sure that we get the concept of half-life:

In 2000, you buried 15 kg of Carbon-14 in your backyard.  Someone digs it up in the year 13,460.  How much Carbon-14 did they find?

OK, That's 11,460 years (which is two half-lives...)

After 5730 years, there'd be 7.5 kg.

After 5730 more years, there'd be 3.75 kg.

Now, let's do one with the formula:

You discovered a new radioactive isotope and named it boogonium (don't ask).  It's half life is 1.23 years.   If you start with a sample of 45 grams, how much will be left in 6.7 years?

A = A not * 2^( -t / h )

A not = 45 grams

t = 6.7 years

h = 1.23 years

Plug this stuff in!

A = 45 * 2^( -6.7 / 1.23 )

Grab a calculator!

A = approximately 1.03 grams

 

YOUR TURN:

An alien radioactive isotope has a half-life of 238 years.  If you start with a sample of 8 kg, how much will be left in 100 years?