Isotope Stability Introductory Chemistry Tutorial

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

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Stable and Unstable Isotopes of Heavy Elements

A stable isotope is one that does not undergo spontaneous nuclear decay.

An unstable isotope is one that does undergo spontaneous nuclear decay.
Unstable isotopes are also referred to as radioactive isotopes, or radiosotopes, or radioactive nucleides, or radionucleides.

Examples of stable and unstable isotopes are found naturally on Earth.
The table below lists some stable and unstable isotopes (radioisotopes) of a number of different elements heavier than lead:

Notice that lead (atomic number 82) is the heaviest element in the periodic table to have stable isotopes!

Although not listed in the table above, all the transuranic elements (those with atomic number greater than 92) are man-made and all their isotopes are unstable.

An element with atomic number (Z) greater than 82 has no stable isotopes.

Isotope Stability of Light Elements

We saw above that the isotopes of "heavy elements", those with atomic number (Z) greater than 82, have no stable isotopes.

Let's define a "light element" as one with atomic number (Z) less than 20, and see if we can find a pattern to the stability of their isotopes.

We've highlighted the unstable isotopes (radioisotopes or radionucleides) in the table above to make it easier to see them.

The first generalisation we might make is that if the neutron to proton ratio is about 1, then the isotope is likely to be stable.
If we pull out all the isotopes with n/p not close to 1, say those with n/p ≥ 1.29 and those with n/p ≤ 0.775, we can construct a new table as shown below¹:

As a first approximation, we predict that a neutron to proton ratio that is very small or very large will result in an unstable isotope.
Notable exceptions are for the small isotopes ³He and ⁷Li which are both stable.

Unfortunately a number of unstable isotopes have neutron to proton ratios of about 1!
Let's take a closer look at these.

None of these unstable isotopes with neutron to proton ratios close to 1 have even numbers of both protons and neutrons.

We could generalisation and say that if the neutron to proton ratio is close to 1, and the nucleus contains an even number of protons and an even number of neutrons then this isotope is most likely to be stable.

Stability of Isotopes of Other Elements

So far we have made a couple of generalisations about the stability of isotopes:

1. Elements with atomic number (Z) greater than 82 have no stable isotopes.
2. Isotopes of elements with atomic number (Z) less than 20 are likely to be unstable if the neutron to proton ratio is either

   (a) very small

   or

   (b) very large

3. Isotopes of elements with atomic number (Z) less than 20 and with a neutron to proton ratio of close to 1 are more likely to be stable if the nucleus contains an even number of protons and an even number of neutrons.

How good is the generalisation that an isotope is more likely to be stable if it has an even number of protons and an even number of neutrons, and, a neutron to proton ratio close to 1, for atomic numbers between 20 and 82?

First, consider the element technetium (Z=43).
It has an odd number of protons, so we predict from our generalisation that the likelihood of it having stable isotopes is low.
We observe that it has no known stable isotopes.

Similarly, promethium (Z=61) has an odd number of protons, so we would predict from our generalisation that the likelihood of it having stable isotopes is low.
We observe that it has no known stable isotopes.

Let's take a look at the isotopes of Period 4 elements with even atomic numbers that are greater than 20.

Of the 38 isotopes listed above, the generalisation is disobeyed just 5 times.

In general, an isotope with an even number of protons is more likely to be stable than an isotope with an odd number of protons.

If you were to survey the known isotopes of all the elements, you would find that most of the stable isotopes have an even number of protons and an even number of neutrons.

^*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.

Worked Examples of Isotope Stability Problems

(based on the StoPGoPS approach to problem solving in chemistry.)

Question 1. Uranium-235 and uranium-238 both occur naturally.

Which of these isotopes is most likely to be unstable?

1. What have you been asked to do?

   Decide if uranium-235 and/or uranium-238 are unstable isotopes of uranium.

2. What information (data) have you been given?

   Extract the data from the question:

   isotope name: uranium-235

   isotope name: uranium-238

3. What is the relationship between what you know and what you need to find out?

   (1) Elements with atomic number greater than 82 have no known stable isotopes.

   (2) Elements with atomic number ≤ 20 with very large or very small neutron to proton ratios are unstable.

   (3) Elements with even numbers of protons and neutrons are most likely to be stable, elements with odd numbers of protons and neutrons are more likely to be unstable.

4. Use the Periodic Table to find the atomic number for the element uranium and decide if it has any stable isotopes:

   uranium has atomic number (Z) = 92

   Elements with Z > 82 have no known stable isotopes.

   Uranium will have no known stable isotopes.
   Uranium-235 is unstable.
   Uranium-238 is unstable.

5. Is your answer plausible?

   Uranium-235 is used as fuel for nuclear reactors so it must be unstable.
   The radioactive decay of uranium-238 can be used to date rocks, so uranium-238 is an unstable isotope of uranium.

6. State your solution to the problem of which uranium isotope(s) are unstable:

   Uranium-235 is unstable.
   Uranium-238 is unstable.

Question 2. Carbon-12 and carbon-14 both occur naturally.

Which of these isotopes is most likely to be stable?

1. What have you been asked to do?

   Determine whether carbon-12 and/or carbon-14 are stable isotopes of carbon.

2. What information (data) have you been given?

   Extract the data from the question:

   isotope name: carbon-12

   isotope name: carbon-14

3. What is the relationship between what you know and what you need to find out?

   (1) Elements with atomic number greater than 82 have no known stable isotopes.

   (2) Elements with atomic number ≤ 20 with very large or very small neutron to proton ratios are unstable.

   (3) Elements with even numbers of protons and neutrons are most likely to be stable, elements with odd numbers of protons and neutrons are more likely to be unstable.

4. Use the Periodic Table to find the atomic number carbon and decide which isotope(s) are stable:

   carbon: Z = 12

   Since 12 < 20, we need to calculate the ratio of neutrons to protons:

   (i) Calculate the number of neutrons in the nucleus of each isotope:
   number of neutrons = A - Z

   (ii) Calculate the ratio of neutrons to protons in the nucleus of each isotope.

   (iii) If n/p ≈ 1 the isotope is probably stable.

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

5. Is your answer plausible?

   Carbon-12 is the most common isotope of carbon, it is incorporated into living things so it is unlikely to be unstable (otherwise it would be continuously damaging cells).
   Carbon-14 is used to date archeological artefacts because it undergoes nuclear decay, that is, carbon-14 is known to be an unstable isotope.

6. State your solution to the problem of which isotopes of carbon are stable:

   Carbon-12 is a stable isotope of carbon.

Question 3. Two isotopes of mercury are mercury-195 and mercury-196.

Which of these isotopes is most likely to be unstable?

1. What have you been asked to do?

   Determine which mercury isotope(s) is unstable.

2. What information (data) have you been given?

   Extract the data from the question:

   isotope name: mercury-195

   isotope name: mercury-196

3. What is the relationship between what you know and what you need to find out?

   (1) Elements with atomic number greater than 82 have no known stable isotopes.

   (2) Elements with atomic number ≤ 20 with very large or very small neutron to proton ratios are unstable.

   (3) Elements with even numbers of protons and neutrons are most likely to be stable, elements with odd numbers of protons and neutrons are more likely to be unstable.

4. Use the Periodic Table to find the atomic number of mercury then decide which isotope is stable if any:

   Z = 80 (even number of protons)

   20 < 80 < 82 so we need to calculate the number of neutrons in the nucleus of an atom of each isotope:

   (i) number of neutrons = A - Z

   (ii) If number neutrons is even, isotope is more likely to be stable.
   If number of neutrons is odd, isotope is more likely to be unstable.

   Isotope	Atomic Number Z (No. protons)	Mass Number A (no. protons + neutrons)	No. neutrons (A - Z)	odd or even	stability prediction
   mercury-195	80	195	195-80=115	protons:even neutrons:odd	unstable
   mercury-196	80	196	196-80=116	protons:even neutrons:even	stable

5. Is your answer plausible?

   Mercury-195 is man-made isotope with a very short half-life so it is known to be an unstable isotope of mercury.

6. State your solution to the problem of which isotope of mercury is unstable:

   Mercury-195 is an unstable isotope of mercury.