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Isotope Stability Chemistry Tutorial

Key Concepts

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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:

Element Atomic Number (Z) Stable Isotope(s) Radioisotope(s)
lead 82 lead-204
lead-206
lead-207
lead-208
lead-202
lead-203
lead-205
lead-210
bismuth 83   bismuth-205
bismuth-206
bismuth-207
bismuth-208
bismuth-209
bismuth-210
polonium 84   polonium-206
polonium-208
polonium-209
polonium-210
radon 86   radon-222
radium 88   radium-223
radium-224
radium-225
radium-226
radium-228
actinium 89   actinium-225
actinium-226
actinium-227
thorium 90   thorium-227
thorium-228
thorium-229
thorium-230
thorium-231
thorium-232
thorium-234
protactinium 91   protactinium-229
protactinium-230
protactinium-231
protactinium-232
protactinium-233
uranium 92   uranium-230
uranium-231
uranium-232
uranium-233
uranium-234
uranium-235
uranium-236
uranium-237
uranium-238

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.

Some Transuranic Elements
Element Atomic Number (Z) Stable Isotopes Radioisotopes
neptunium 93   234Np, 235Np, 236Np, 237Np, 238Np, 239Np
plutonium 94   236Pu, 237Pu, 238Pu, 239Pu, 240Pu, 241Pu, 242Pu, 244Pu, 246Pu, 247Pu
americium 95   240Am, 241Am, 242Am, 243Am
curium 96   240Cm, 241Cm, 242Cm, 243Cm, 244Cm, 245Cm, 246Cm, 247Cm, 248Cm, 250Cm
berkelium 97   245Bk, 246Bk, 247Bk, 248Bk, 249Bk
californium 98   246Cf, 248Cf, 249Cf, 250Cf, 251Cf, 252Cf, 253Cf, 254Cf
einsteinium 99   251Es, 252Es, 253Es, 254Es, 255Es
fermium 100   252Fm, 253Fm, 257Fm
mendelevium 101   258Md, 260Md

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

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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.

Element Atomic Number (Z)
No. Protons
Stable Isotopes Radioisotopes No. Neutrons No. Neutrons/No. Protons
hydrogen 1 1H   0 0/1 = 0
2H   1 1/1 = 1
  3H 2 2/1 = 2
helium 2 3He   1 1/2 = 0.5
4He   2 2/2 = 1
lithium 3 6Li   3 3/3 = 1
7Li   4 4/3 = 1.3
beryllium 4   7Be 3 3/4 = 0.75
9Be   5 5/4 = 1.25
  10Be 6 6/4 = 1.5
boron 5 10B   5 5/5 = 1
11B   6 6/5 = 1.2
carbon 6 12C   6 6/6 = 1
13C   7 7/6 = 1.17
  14C 8 8/6 = 1.3
nitrogen 7 14N   7 7/7 = 1
15N   8 8/7 = 1.14
oxygen 8 16O   8 8/8 = 1
17O   9 9/8 = 1.125
18O   10 10/8 = 1.23
fluorine 9 19F   10 10/9 = 1.11
neon 10 20Ne   10 10/10 = 1
21Ne   11 11/10 = 1.1
22Ne   12 12/10 = 1.2
sodium 11   22Na 11 11/11 = 1
23Na   12 12/11 = 1.09
magnesium 12 24Mg   12 12/12 = 1
25Mg   13 13/12 = 1.08
26Mg   14 14/12 = 1.17
aluminium 13   26Al 13 13/13 = 1
27Al   14 14/13 = 1.08
silicon 14 28Si   14 14/14 = 1
29Si   15 15/14 = 1.07
30Si   16 16/14 = 1.14
  32Si 18 18/14 = 1.29
phosphorus 15 31P   16 16/15 = 1.07
  32P 17 17/15 = 1.13
  33P 18 18/15 = 1.2
sulfur 16 32S   16 16/16 = 1
33S   17 17/16 = 1.06
34S   18 18/16 = 1.125
  35S 19 19/16 = 1.1875
36S   20 20/16 = 1.25
chlorine 17 35Cl   18 18/17 = 1.06
  36Cl 19 19/17 = 1.11
37Cl   20 20/17 = 1.18
argon 18 36Ar   18 18/18 = 1
  37Ar 19 19/18 = 1.06
38Ar   20 20/18 = 1.1
  39Ar 21 21/18 = 1.17
40Ar   22 22/18 = 1.2
  42Ar 24 24/18 = 1.3
potassium 19 39K   20 20/19 = 1.05
  40K 21 21/19 = 1.1
41K   22 22/19 = 1.16
calcium 20 40Ca   20 20/20 = 1
  41Ca 21 21/20 = 1.05
42Ca   22 22/20 = 1.1
43Ca   23 23/20 = 1.15
44Ca   24 24/20 = 1.2
  45Ca 25 25/20 = 1.25
46Ca   26 26/20 = 1.3
  47Ca 27 27/20 = 1.35
  48Ca 28 28/20 = 1.4

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:

n/p ≤ 0.775 or n/p ≥ 1.29
stable isotope unstable isotope
  3H
3He  
7Li  
  10Be
  14C
  32Si
  42Ar
46Ca  
  47Ca
  48Ca

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.

n/p ≈ 1
unstable isotope no. protons
(Z)
no. neutrons
22Na 11 11
26Al 13 13
32P 15 17
33P 15 18
35S 16 19
36Cl 17 19
37Ar 18 19
39Ar 18 21
40K 19 21
41Ca 20 21
45Ca 20 25

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.

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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.

Period 4 Elements
element Z stable isotopes unstable isotopes
Ti 22 46Ti, 48Ti, 50Ti 44Ti (n/p = 1)
Cr 24 50Cr, 52Cr, 54Cr  
Fe 26 54Fe, 56Fe, 58Fe 60Fe (n/p = 1.3)
Ni 28 58Ni, 60Ni, 62Ni, 64Ni 56Ni (n/p = 1), 66Ni (n/p = 1.36)
Zn 30 64Zn, 66Zn, 68Zn, 70Zn 72Zn (n/p = 1.4)
Ge 32 70Ge, 72Ge, 74Ge 68Ge (n/p = 1.1), 76Ge (n/p = 1.4)
Se 34 74Se, 76Se, 78Se, 80Se 72Se (n/p = 1.1), 82Se (n/p = 1.4)
Kr 36 80Kr, 82Kr, 84Kr, 86Kr 78Kr (n/p = 1.2)

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.

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.

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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.


Footnotes:

1. These numbers are completely arbitrary. Choosing different n/p ratios to represent "close to 1" will result in different isotopes being "inside" and "outside" the range.