Unit 4 - Mark Rosengarten

3) Half-Life (HW: p. 24, 25)
Essential Question: How exactly do we know how old archeological remains are? How can radioactivity save your
life?
Radioactive Decay is a RANDOM process. It is not possible to predict when a particular nucleus will decay, but we
can make fairly accurate predictions regarding how many nuclei in a large sample will decay in a given period of time.
Definition of Half-Life:
The half-life of a radioactive isotope is defined as the period of time that must go by for half of the nuclei in the sample
to undergo decay. During one half-life period:
- Half of the radioactive nuclei in the sample decay into new, more stable nuclei
If a sample contains 1000 nuclei of a radioactive isotope now, 500 will undergo decay over the course of one half-life.
- Half the mass of the radioactive isotope is converted into a new, more stable isotope
If a sample contains 4.0 grams of a radioactive isotope now, after one half-life, 2.0 grams will remain undecayed, the
other 2.0 grams will be made up of a new, more stable isotope.
- A Geiger-Müeller counter’s count-per-time period will be half of what it started at
If a Geiger-Müeller counter is showing 400 counts per minute now, after one half-life, the counter will show 200 counts
per minute.
After one half-life, half (50%) of the original amount of the sample will have undergone radioactive decay.
After a second half-life, one quarter (25%) of the original sample will remain undecayed.
After a third half-life, one eighth (12.5%) of the original sample will remain undecayed.
NOTE: The actual half-life time is constant. If the half-life is 10 days, then 2 half-lives would take 20 days, 3
half-lives take 30 days, 4 half-lives take 40 days and so on.
The half-life of many radioactive isotopes can be found on Reference Table N.
SOLVING HALF – LIFE PROBLEMS
1) You know how much of the isotope you have now, you want to find out how much will be left after a certain
amount of time (going into the future).
Step 1: Determine how many half-lives have gone by. Take how much time has gone by and divide it by the duration
of the half-life.
Step 2: Cut the amount (mass, percent, fraction, number of nuclei) in half as many times as there are half-lives.
EXAMPLES:
The half-life of Rn-222 (a carcinogenic house pollutant) is 3.8 days. If today your basement contains 20.0
grams of Rn-222, how much will remain after 19 days assuming no more leaks in?
# half-lives = time elapsed/half-life time = 19 days/3.8 days = 5 half-lives have gone by.
So, cut the starting amount (20.0 grams) in half 5 times!
20.0 10.0 5.0 2.5 1.25 0.625 grams is the final amount left!
© 2011, Mark Rosengarten R 10