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 halflife 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:
Element 
Atomic Number (Z) 
Stable Isotope(s) 
Radioisotope(s) 
lead 
82 
lead204 lead206 lead207 lead208 
lead202 lead203 lead205 lead210 
bismuth 
83 

bismuth205 bismuth206 bismuth207 bismuth208 bismuth209 bismuth210 
polonium 
84 

polonium206 polonium208 polonium209 polonium210 
radon 
86 

radon222 
radium 
88 

radium223 radium224 radium225 radium226 radium228 
actinium 
89 

actinium225 actinium226 actinium227 
thorium 
90 

thorium227 thorium228 thorium229 thorium230 thorium231 thorium232 thorium234 
protactinium 
91 

protactinium229 protactinium230 protactinium231 protactinium232 protactinium233 
uranium 
92 

uranium230 uranium231 uranium232 uranium233 uranium234 uranium235 uranium236 uranium237 uranium238 
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 manmade and all their isotopes are unstable.
Some Transuranic Elements 
Element 
Atomic Number (Z) 
Stable Isotopes 
Radioisotopes 
neptunium 
93 

^{234}Np, ^{235}Np, ^{236}Np, ^{237}Np, ^{238}Np, ^{239}Np 
plutonium 
94 

^{236}Pu, ^{237}Pu, ^{238}Pu, ^{239}Pu, ^{240}Pu, ^{241}Pu, ^{242}Pu, ^{244}Pu, ^{246}Pu, ^{247}Pu 
americium 
95 

^{240}Am, ^{241}Am, ^{242}Am, ^{243}Am 
curium 
96 

^{240}Cm, ^{241}Cm, ^{242}Cm, ^{243}Cm, ^{244}Cm, ^{245}Cm, ^{246}Cm, ^{247}Cm, ^{248}Cm, ^{250}Cm 
berkelium 
97 

^{245}Bk, ^{246}Bk, ^{247}Bk, ^{248}Bk, ^{249}Bk 
californium 
98 

^{246}Cf, ^{248}Cf, ^{249}Cf, ^{250}Cf, ^{251}Cf, ^{252}Cf, ^{253}Cf, ^{254}Cf 
einsteinium 
99 

^{251}Es, ^{252}Es, ^{253}Es, ^{254}Es, ^{255}Es 
fermium 
100 

^{252}Fm, ^{253}Fm, ^{257}Fm 
mendelevium 
101 

^{258}Md, ^{260}Md 
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.
Element 
Atomic Number (Z) No. Protons 
Stable Isotopes 
Radioisotopes 
No. Neutrons 
No. Neutrons/No. Protons 
hydrogen 
1 
^{1}H 

0 
0/1 = 0 
^{2}H 

1 
1/1 = 1 

^{3}H 
2 
2/1 = 2 
helium 
2 
^{3}He 

1 
1/2 = 0.5 
^{4}He 

2 
2/2 = 1 
lithium 
3 
^{6}Li 

3 
3/3 = 1 
^{7}Li 

4 
4/3 = 1.3 
beryllium 
4 

^{7}Be 
3 
3/4 = 0.75 
^{9}Be 

5 
5/4 = 1.25 

^{10}Be 
6 
6/4 = 1.5 
boron 
5 
^{10}B 

5 
5/5 = 1 
^{11}B 

6 
6/5 = 1.2 
carbon 
6 
^{12}C 

6 
6/6 = 1 
^{13}C 

7 
7/6 = 1.17 

^{14}C 
8 
8/6 = 1.3 
nitrogen 
7 
^{14}N 

7 
7/7 = 1 
^{15}N 

8 
8/7 = 1.14 
oxygen 
8 
^{16}O 

8 
8/8 = 1 
^{17}O 

9 
9/8 = 1.125 
^{18}O 

10 
10/8 = 1.23 
fluorine 
9 
^{19}F 

10 
10/9 = 1.11 
neon 
10 
^{20}Ne 

10 
10/10 = 1 
^{21}Ne 

11 
11/10 = 1.1 
^{22}Ne 

12 
12/10 = 1.2 
sodium 
11 

^{22}Na 
11 
11/11 = 1 
^{23}Na 

12 
12/11 = 1.09 
magnesium 
12 
^{24}Mg 

12 
12/12 = 1 
^{25}Mg 

13 
13/12 = 1.08 
^{26}Mg 

14 
14/12 = 1.17 
aluminium 
13 

^{26}Al 
13 
13/13 = 1 
^{27}Al 

14 
14/13 = 1.08 
silicon 
14 
^{28}Si 

14 
14/14 = 1 
^{29}Si 

15 
15/14 = 1.07 
^{30}Si 

16 
16/14 = 1.14 

^{32}Si 
18 
18/14 = 1.29 
phosphorus 
15 
^{31}P 

16 
16/15 = 1.07 

^{32}P 
17 
17/15 = 1.13 

^{33}P 
18 
18/15 = 1.2 
sulfur 
16 
^{32}S 

16 
16/16 = 1 
^{33}S 

17 
17/16 = 1.06 
^{34}S 

18 
18/16 = 1.125 

^{35}S 
19 
19/16 = 1.1875 
^{36}S 

20 
20/16 = 1.25 
chlorine 
17 
^{35}Cl 

18 
18/17 = 1.06 

^{36}Cl 
19 
19/17 = 1.11 
^{37}Cl 

20 
20/17 = 1.18 
argon 
18 
^{36}Ar 

18 
18/18 = 1 

^{37}Ar 
19 
19/18 = 1.06 
^{38}Ar 

20 
20/18 = 1.1 

^{39}Ar 
21 
21/18 = 1.17 
^{40}Ar 

22 
22/18 = 1.2 

^{42}Ar 
24 
24/18 = 1.3 
potassium 
19 
^{39}K 

20 
20/19 = 1.05 

^{40}K 
21 
21/19 = 1.1 
^{41}K 

22 
22/19 = 1.16 
calcium 
20 
^{40}Ca 

20 
20/20 = 1 

^{41}Ca 
21 
21/20 = 1.05 
^{42}Ca 

22 
22/20 = 1.1 
^{43}Ca 

23 
23/20 = 1.15 
^{44}Ca 

24 
24/20 = 1.2 

^{45}Ca 
25 
25/20 = 1.25 
^{46}Ca 

26 
26/20 = 1.3 

^{47}Ca 
27 
27/20 = 1.35 

^{48}Ca 
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 below^{1}:
n/p ≤ 0.775 or n/p ≥ 1.29 
stable isotope 
unstable isotope 

^{3}H 
^{3}He 

^{7}Li 


^{10}Be 

^{14}C 

^{32}Si 

^{42}Ar 
^{46}Ca 


^{47}Ca 

^{48}Ca 
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 ^{3}He and ^{7}Li 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 
^{22}Na 
11 
11 
^{26}Al 
13 
13 
^{32}P 
15 
17 
^{33}P 
15 
18 
^{35}S 
16 
19 
^{36}Cl 
17 
19 
^{37}Ar 
18 
19 
^{39}Ar 
18 
21 
^{40}K 
19 
21 
^{41}Ca 
20 
21 
^{45}Ca 
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.
Stability of Isotopes of Other Elements
So far we have made a couple of generalisations about the stability of isotopes:
 Elements with atomic number (Z) greater than 82 have no stable isotopes.
 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
 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 
^{46}Ti, ^{48}Ti, ^{50}Ti 
^{44}Ti (n/p = 1) 
Cr 
24 
^{50}Cr, ^{52}Cr, ^{54}Cr 

Fe 
26 
^{54}Fe, ^{56}Fe, ^{58}Fe 
^{60}Fe (n/p = 1.3) 
Ni 
28 
^{58}Ni, ^{60}Ni, ^{62}Ni, ^{64}Ni 
^{56}Ni (n/p = 1), ^{66}Ni (n/p = 1.36) 
Zn 
30 
^{64}Zn, ^{66}Zn, ^{68}Zn, ^{70}Zn 
^{72}Zn (n/p = 1.4) 
Ge 
32 
^{70}Ge, ^{72}Ge, ^{74}Ge 
^{68}Ge (n/p = 1.1), ^{76}Ge (n/p = 1.4) 
Se 
34 
^{74}Se, ^{76}Se, ^{78}Se, ^{80}Se 
^{72}Se (n/p = 1.1), ^{82}Se (n/p = 1.4) 
Kr 
36 
^{80}Kr, ^{82}Kr, ^{84}Kr, ^{86}Kr 
^{78}Kr (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 hydrogen2, lithium6, boron10 and nitrogen14.
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.
Uranium235 and uranium238 both occur naturally.
Which of these isotopes is most likely to be unstable?
 What have you been asked to do?
Decide if uranium235 and/or uranium238 are unstable isotopes of uranium.
 What information (data) have you been given?
Extract the data from the question:
isotope name: uranium235
isotope name: uranium238
 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.
 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.
Uranium235 is unstable.
Uranium238 is unstable.
 Is your answer plausible?
Uranium235 is used as fuel for nuclear reactors so it must be unstable.
The radioactive decay of uranium238 can be used to date rocks, so uranium238 is an unstable isotope of uranium.
 State your solution to the problem of which uranium isotope(s) are unstable:
Uranium235 is unstable.
Uranium238 is unstable.
Question 2.
Carbon12 and carbon14 both occur naturally.
Which of these isotopes is most likely to be stable?
 What have you been asked to do?
Determine whether carbon12 and/or carbon14 are stable isotopes of carbon.
 What information (data) have you been given?
Extract the data from the question:
isotope name: carbon12
isotope name: carbon14
 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.
 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 
carbon12 
6 
12 
12  6 = 6 
6/6 = 1 
stable 
carbon14 
6 
14 
14  6 = 8 
8/6 = 1.3 
unstable 
 Is your answer plausible?
Carbon12 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).
Carbon14 is used to date archeological artefacts because it undergoes nuclear decay, that is, carbon14 is known to be an unstable isotope.
 State your solution to the problem of which isotopes of carbon are stable:
Carbon12 is a stable isotope of carbon.
Question 3.
Two isotopes of mercury are mercury195 and mercury196.
Which of these isotopes is most likely to be unstable?
 What have you been asked to do?
Determine which mercury isotope(s) is unstable.
 What information (data) have you been given?
Extract the data from the question:
isotope name: mercury195
isotope name: mercury196
 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.
 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 
mercury195 
80 
195 
19580=115 
protons:even neutrons:odd 
unstable 
mercury196 
80 
196 
19680=116 
protons:even neutrons:even 
stable 
 Is your answer plausible?
Mercury195 is manmade isotope with a very short halflife so it is known to be an unstable isotope of mercury.
 State your solution to the problem of which isotope of mercury is unstable:
Mercury195 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.