Half-life and Carbon

Question

A radioactive isotope at time t is 1/2 ^ t/t(half-life). The halflife of carbon 14 is 5730 yrs. What fraction of carbon 14 in a piece of charcoal remains after 19.0 yrs 1.600 x 10^4 yrs and 1.8000 x 10^5 yrs ? 

Answer 1

Chris,

 

They are all done the same.   1/2 of the substance

you start with will be there after 5730 years, that is

why it is called half life.

 

For each part of your question, you have to find

how many half lives have taken place, that is why 

you divide your years by 5730.

 

After getting that number, you will take "1/2" to

that power.

 

Here is one that appears harder to see than the others:

 

amount (after 1.8000 x 10^5 years) = (1/2)^[(1.8000x10^5)/5730]

 

                                        amount = 3.4959 x 10^(-10)

 

Just plug in values for the "t" in the exponent's numerator

and let your calculator do the work!