Here we will go over why isotopes undergo nuclear decay and how to use that to determine the age of a sample.

1. Nuclear Stability and Decay
• More than 1500 different isotopes are known. Of
those, only 264 are stable and do not decay over time.
• One factor that affects the stability of nucleus is the
ratio of neutrons to protons.
• Too many or too few neutrons relative to the number
of protons makes the nucleus unstable.
• A neutron vs proton plot of stable nuclei form a
pattern called the band of stability.

2. Band of Stability

3. • For elements with atomic numbers 20 or less, this
ratio is about 1:1. Above atomic number 20, stable
nuclei have more neutrons than protons.
• The band of stability can be explained by the
relationship between the nuclear force and the
electrostatic forces between protons.
– As the number of protons in a nucleus increases, the
repulsive electrostatic force between protons increases
faster than the nuclear force.
– More neutrons are required to increase the nuclear force
and stabilize the nucleus.
– Beyond the atomic number 83, bismuth, the
repulsive force of the protons is so great that
no stable isotopes exists.

5. Half-Life
– Every radioisotope has a characteristic rate of
decay, which is measured by its half-life.
– Half-life is the time required for one-half of the nuclei
in a radioisotope sample to decay.
– During each half-life, half of the remaining
radioactive atoms decay into atoms of a new
element.
– Each radioactive nuclide has its own half-life. Half-
lives can be a short as a fraction of a second or as
long as billions of years.

7. • One isotope that has a long half-life is uranium-238.
– 4.5 billion years
– decays through a complex series of unstable
isotopes to the stable isotope of lead-206.

8. Decay Series of U-238
Stable Isotope

9. – The following equation can be used to calculate
how much of an isotope will remain after a given
number of half-lives.
A = Ao x (1/2)n
• A stands for the amount remaining, Ao for the
initial amount, and n for the number of half-
lives.

10. Half-Life Sample Problem
Phosphorus-32 has a half-life of 14.3 days.
a) How long is four half-lives?
b) If you started with 24.0 g of phosphorus-32, how
many grams of the isotope remain at the end four
half-lives?

11. Outcome Sentences
• After reflecting on
today’s lesson,
complete three of the
sentence starters.
• Sentence Starters
– I’ve learned…
– I was surprised…
– I’m beginning to wonder…
– I would conclude…
– I now realize that…