1 Nuclear Stability and Magic Numbers
Nuclear Stability and Magic Numbers
Nuclear Stability is a concept that helps to identify the stability of an isotope. In
order to identify the stability of an isotope or also known as the nuclei, you need to
find the ratio of neutrons to protons.
Contents
1. Introduction
2. Concepts
3. Belt of stability
4. Magic Numbers:
5. Stable or Unstable?
6. Outside links
7. References
8. Problems
Introduction
An isotope is an element that has same atomic number but different atomic mass
compared to the periodic table. Every element has a proton, neutron, and electron.
The number of protons is equal to the atomic number, and the number of electrons
is equal the protons, unless it is an ion. To determine the number of neutrons in an
element you subtract the atomic number from the atomic mass of the element.
Atomic mass is represented as (A) and atomic number is represented as (Z) and
neutrons are represented as (N).
A-Z=N
(atomic mass )-(atomic number)= number of neutrons
To determine the stability of an isotope you can use the ratio neutron/proton (N/Z).
Also to help understand this concept there is a graph called the Belt of Nuclear
stability. This graph is a plot of all the stable nuclei. The graph consists of a y-axis
labeled neutrons, an x-axis labeled protons, and a nuclei. On the graph it is easier
to determine where the alpha decay, beta decay, and positron emission or electron
capture occurs.
Concepts
Determine ratio:
To determine the ratio you use the equation: N/Z
2 Nuclear Stability and Magic Numbers
Elements that have an atomic number (Z) lower than 20 are lighter and these
elements' nuclei and have a ratio of 1:1. These elements prefer to have the same
amount of protons and neutrons.
example: carbon-12 and oxygen-16
Carbon: A-Z=N; 12-6= 6 ; 1:1 ratio (because there are 6 protons and 6 neutrons).
Oxygen: A-Z= N; 16-8=8 1:1 ratio (because there are 8 protons and 8 neutrons).
Elements that have atomic numbers from 20 to 83 are heavy elements, therefore
the ratio is different. The ratio is 1.5:1, the reason for this difference is because of
the repulsive force between protons: the stronger the repulsion force, the more
neutrons are needed to stabilize the nuclei.
Belt of stability
Note: This graph is not accurate, just an example of how the graph should look and the different terms to
know.
3 Nuclear Stability and Magic Numbers
The graph has a plot of stable elements, this part is called band of stability. At the
higher end of the band of stability lies alpha decay, below is positron emission or
electron capture, above is beta emissions and elements beyond the atomic mass of
83 are unstable radioactive elements.
Alpha decay is located at the top of the plotted line, because the alpha decay
decreases the mass number of the element in order to keep the isotope stable. This
is done by using the element helium (He). An unstable isotope's protons are
decreased by 2 and its neutrons are decreased by 4, and because the isotope was
originally unstable before it went through alpha decay, the elements are still
considered unstable.
Beta decay accepts protons so it changes the amount of protons and neutrons. The
number of protons increases while neutrons decrease. To make things easier to
understand think of the ratio of the isotope: there are too many neutrons compared
to the number of protons therefore it is above the band of stability.
Positron emission and electron capture is when the isotope gains more neutrons.
Positron emission and electron capture are below the band of stability because the
ratio of the isotope has more protons than neutrons, think of it as there are too few
protons for the amount of neutrons and that is why it is below the band of stability.
Magic Numbers:
Magic numbers are natural occurrences in isotopes and are stable. Below is a list of
numbers of protons and neutrons; isotopes that have these numbers occurring in
either the proton or neutron are stable. In some cases there the isotopes can consist
of magic numbers for both protons and neutrons; these would be called double
magic numbers. But the double numbers only occur for isotopes that are heavier,
because the repulsion of the forces between the protons.
The magic numbers:
proton: 2, 8, 20, 28, 50, 82, 114
neutron: 2, 8, 20, 28, 50, 82, 126, 184
Also, there is the concept that isotopes consisting of a combination of even-even,
even-odd, odd-even, and odd-odd are all stable. There are more nuclides that have
a combination of even-even than odd-odd. (See chart.)
4 Nuclear Stability and Magic Numbers
Examples of the odd-odd nuclides:
Stable or Unstable?
Here is a simple chart that can help you decide if an element is stable:
Figure (left)-The
contents of this
figure has been
taken from a
lecture by Jim
Hollister, LSC
Outside links


http://employees.oneonta.edu/viningwj/sims/stability_of_isotopes_s.swf -Go to
this website to see a more accurate graph of belt of stability
http://teachertube.com/viewVideo.php?video_id=139403&title=Nuclear_Stabilit
y -This video goes over nuclear stability and the types of radio active decay
References
1. Olmsted III, John and Gregory M William. Chemistry Fourth Edition. John Wiley
and Sons Inc:NJ, 2006.
2. Petrucci, Ralph H., William S. Harwood, F. Geoffrey Herring, Jeffry D
Madura. General Chemistry. Pearson Education Inc: NJ, 2007.
5 Nuclear Stability and Magic Numbers
Problems
1) Using the above chart state if this isotope is alpha-emitter, stable, or
unstable: a) 4020Ca b) 5425Mn c) 21084 Po
2) If the isotope is located above the band of stability what type of radioactivity is
it? what if it was below?
3) Between elements bromide and carbon which is more stable when using magic
numbers?
4) Name one of the isotopes that consist of odd-odd combination in the nuclei?
Answers: 1) a) Stable, because this Ca isotope has 20 neutrons, which is on of the
magic numbers
b) Unstable, because there is an odd number (25 and 29) of protons and
neutrons
c) Alpha-emitter, because Z=84, which follows rule/step one on the chart
2) Beta decay, positron emission, or electron capture
3) Carbon is stable
4) Hydrogen-2, Lithium-6, Boron-10, nitrogen-14