I could use some help with the following question.
The half-life of is 5730 years. If a sample of has a mass of 20 micrograms at time 0, how long will it take until (a) 10 micrograms, and (b) 5 micrograms are left.
Here's what I have:
To solve, I use the exponential decay formula:
First, I solve for k:
But, here I am stuck, because the value of is a very long non-terminating decimal. How am I supposed to use this in the exponential decay formula?
This problem is a lot easier than you are making it out to be! You just need to understand what the definition of "half life" is - then the answers become obvious. The half-life is the time it takes for the concentration of particles to be reduced by half from the original. If you start with 20 micrograms of C14, and its half-life is 5730 years, that means that after 5730 years you will have half or 20 grams, or 10 micrograms of C14. If you wait another 5730 years after that, the 10 micrograms is reduced to 5. So the answers are obvious.
If you want to see how the math works - you need to use the correct formula. The correct formula is:
where k is the half life. So for the first question:
t = 5730.
Are you using a calculator to do this? Most calculators today have the ability to store numbers and it would be better to keep the number in calculator memory rather than writing it down and keeping all decimal places.