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The elements you see in the periodic table are all of the elements there are. What you don’t see are all the isotopes. As you know, atoms belong to one element or another based on the number of protons in their nuclei. Atoms with six protons in their nuclei are atoms of carbon.

Carbon has two common isotopes: carbon-12 (¹²C) and carbon-13 (¹³C). The number that is superscripted to the left of the atomic symbol is the atomic mass number. It tells you the approximate mass of a particular isotope. Recall that isotopes are atoms of an element with different numbers of neutrons. Isotopes can be told apart by their mass numbers. The mass number (A) equals the sum of the number of protons and neutrons (A = Z + n⁰).

Fill in the following table with the required information about the isotopes in the picture at left.

Name	Symbol	p+	n0	Mass
hydrogen-1	1 1H	1	0	1

The above is an image showing all of the known isotopes. Each speck represents one isotope. The black specks running down the middle represent the stable isotopes. What are stable isotopes? Those are atoms that do not emit radiation. Stable isotopes are like a solidly built skyscraper: they are made to withstand the pressure of high winds and the shaking of earthquakes. Stable isotopes are built to withstand the outward push of the protons: since they all have a positive charge, they push against each other to get away. The strong nuclear force pulls them back in but they need neutrons to get enough strong nuclear force to keep them from flying apart.

 

The more protons there are in an atom (the higher the atomic number) the more neutrons are needed to keep the atom from flying apart. Take a look at the following graph:

The graph shows atomic number (Z) across the x-axis and number of neutrons (A – Z) along the y-axis. Remember, Z + n⁰ = A, (A is the atomic mass number).

The line on the graph represents the places on the graph where p⁺ = n⁰. This is the same as saying Z = A – Z.

All the specks on the graph represent isotopes. The stable isotopes are always in the middle of the crowd, so to speak. For low numbers of protons

Electric Forces

+ <—> +

+ >–< –

– <—> –

(low Z) the number of protons and neutrons is fairly equal. At first, there is a one-to-one ratio. As Z climbs higher, more and more neutrons appear to be needed in order to make the atomic nuclei stable.

How do we explain this? There are two forces at work: electrostatic forces and the strong nuclear force. The electrostatic force makes the protons in the nucleus try to fly away from one another. Positive charges repel each other; positive and negative charges are attracted to one another; and negative charges repel each other. Protons are positive and are repeled from one another. The electrostatic force has no effect on neutrons. (Why?) The closer two particles are, the stronger the electrostatic force between them.

The strong nuclear force acts on protons and neutrons and pays no attention to charge. It acts over very small distances (1 × 10^-15 m) and makes nuclear particles stick together. The more nuclear particles (protons and neutrons) there are, the stronger the strong nuclear force is.

There are two kinds of unstable nucleus. One, there are too few neutrons to balance the electrostatic repulsion of the protons. Two, there are too many neutrons and the nucleus is crushed together so much that the protons are repelled more strongly. Either way, the nucleus is unstable. This is the origin of radioactivity.

Questions

9. Look at the graph of Z vs. A – Z. Write down how many neutrons (approximately) are needed to make the following elements stable:
   1. element 4
   2. Z = 25
   3. Zr
   4. element 79
   5. lead
10. Approximately where on that graph does the zone of stability diverge from a 1:1 ratio?
11. Explain this divergence.
12. No elements above Z = 83 have any stable isotopes. Why do you think that is?

13. Look at the chart below. How many isotopes of carbon are there? Which ones are stable? Write both the name and the symbol for each stable isotope.
14. How many isotopes of hydrogen are there? Which ones are stable? Write both the name and the symbol for all of the isotopes.
15. Write down the ratio of protons to neutrons for all the isotopes from hydrogen-1 to lithium-11.

    symbol

    mass

    p+

    n0

    ratio

16. What pattern do you see? Which ratios correspond to stable isotopes? To unstable isotopes?