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.

Band of Stability

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.

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.

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.

Decay Series of U-238 Stable Isotope

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

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?

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…