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Isotope Stability

Key Concepts

An unstable isotope emits some kind of radiation, that is it is radioactive.
A stable isotope is one that does not emit radiation, or, if it does its half-life is too long to have been measured.
It is believed that the stability of the nucleus of an isotope is determined by the ratio of neutrons to protons.
Observations of the atomic number of isotopes show us that:

Isotopes with atomic number (Z) > 82 are unstable
Of the elements with atomic number (Z) < 82, all have one or more stable isotopes except technetium (Z = 43) and promethium (Z = 61) which do not have any stable isotopes.
Isotopes with atomic number (Z) ≤ 20 and with a neutron (n) to proton (p) ratio of about 1 are more likely to be stable (n ÷ p ~ 1)

Observations on whether the nucleus contains odd or even numbers of protons and neutrons leads us to believe that a nucleus with:

odd numbers of protons and odd numbers of neutrons is most likely to be unstable
even number of protons and even numbers of neutrons is most liklely to be stable

Composition of the Nucleii of Known Stable Isotopes

Protons Neutrons % Stable Isotopes Stability Trend

odd odd 1.5%^* least stable

odd even 18% ↓

even odd 20.5% ↓

even even 60% most stable

^*Stable nucleii with an odd number of protons and an odd number of neutrons are hydrogen-2, lithium-6, boron-10 and nitrogen-14. Each of these has Z < 20 and a neutron:proton ratio of 1.

Predicting the Stability of an Isotope

Example 1
Uranium-235 and uranium-238 both occur naturally.
Which of these isotopes is most likely to be unstable?

Use the Periodic Table to find the atomic number (Z) for uranium
Z = 92
Predict the stability of each isotope:
Since the atomic number for uranium is greater than 82, both isotopes are predicted to be unstable.

Example 2
Carbon-12 and carbon-14 both occur naturally.
Which of these isotopes is most likely to be stable?

Use the Periodic Table to find the atomic number, Z, for carbon:
Z = 6

Predict stability:
Since Z < 20, the most stable isotope is the one whose ratio of neutrons (n) to protons (p) is close to 1 (n ÷ p ~ 1)

Isotope	Atomic Number Z (No. protons)	Mass Number A (no. protons + neutrons)	No. neutrons (A - Z)	n/p	stability
carbon-12	6	12	12-6=6	6/6=1	stable
carbon-14	6	14	14-6=8	8/6=1.3	unstable

Example 3
Two isotopes of mercury are mercury-195 and mercury-196.
Which of these isotopes is most likely to be stable?

Use the Periodic Table to find the atomic number, Z, for mercury (Hg):
Z = 80

Since Z for mercury is greater than 20 but less than 82, we will need to rely on a comparision of odd and even numbers of protons and neutrons in each nucleus: