D. Energy and Society · Thermal and Nuclear EnergyThe Nucleus and Isotopes
D3.9 D2.1 A2.2About 65 minutes
Learning goals- I can describe the structure of a nucleus using protons, neutrons, mass number and atomic number.
- I can write and read nuclear notation such as ²³⁵₉₂U.
- I can identify and describe the isotopes of hydrogen: protium, deuterium and tritium.
- I can explain the role of the strong nuclear force and why heavy nuclei need extra neutrons.
Words to know
nucleon
A proton or a neutron (a particle found in the nucleus).
atomic number (Z)
The number of protons in a nucleus. It identifies the element.
mass number (A)
The total number of protons and neutrons in a nucleus.
isotopes
Atoms of the same element (same Z) with different numbers of neutrons (different A).
deuterium / tritium
Hydrogen-2 (1 proton, 1 neutron) and hydrogen-3 (1 proton, 2 neutrons). Tritium is radioactive.
heavy water (D₂O)
Water made with deuterium instead of ordinary hydrogen. CANDU reactors use it.
strong nuclear force
A very strong, very short-range attraction between nucleons that holds the nucleus together.
Glowing exit signs and heavy water
Some exit signs in schools and arenas glow green all night with no electricity at all. Inside each sign are small glass tubes containing a gas called tritium: a form of hydrogen whose nucleus is unstable and slowly gives off radiation, which makes a coating in the tube glow.
Tritium is hydrogen, the same element that makes up water. So how can hydrogen be radioactive? The answer is in the nucleus, and it is the starting point for everything in the second half of this unit: radioactivity, half-life, fission, fusion and nuclear power.
Remember from Grade 9
In Grade 9 you learned that atoms have a tiny, dense nucleus of protons and neutrons, surrounded by electrons. You learned that isotopes of an element have the same number of protons but different numbers of neutrons (for example carbon-12, carbon-13 and carbon-14), and that some isotopes are radioactive. You also met Ernest Rutherford's gold-foil experiment. Now we look inside the nucleus in more detail.
Describing a nucleus
The nucleus contains two kinds of nucleons:
- Protons: charge +1 (in units of the elementary charge), mass about 1 u (atomic mass unit).
- Neutrons: no charge, mass about 1 u (very slightly more than a proton).
Two numbers describe a nucleus:
- The atomic number, Z = number of protons. Z decides which element it is. Every carbon nucleus has Z = 6; every uranium nucleus has Z = 92.
- The mass number, A = number of protons + number of neutrons.
So the number of neutrons is N = A − Z.
We write a particular nucleus (a nuclide) in nuclear notation: the mass number goes at the top left and the atomic number at the bottom left of the chemical symbol, for example ²³⁵₉₂U. Since the symbol already tells you Z, people often just write uranium-235 or U-235.
The three isotopes of hydrogen
Hydrogen (Z = 1) has three isotopes, important enough to have their own names:
- Protium, ¹H: 1 proton and no neutrons. Over 99.98% of hydrogen atoms.
- Deuterium, ²H or D: 1 proton and 1 neutron. Stable. Roughly 1 in every 6400 hydrogen atoms in ordinary water is deuterium. Water made with deuterium, D₂O, is called heavy water. Canada's CANDU reactors use heavy water to slow down neutrons and to carry heat, as you will see in The CANDU Reactor: Inside a Nuclear Power Plant.
- Tritium, ³H or T: 1 proton and 2 neutrons. Radioactive, with a half-life of about 12.3 years. Tiny amounts form naturally in the upper atmosphere, and CANDU reactors produce tritium in their heavy water. It is used in self-lit exit signs and in fusion research.
All three have one proton and one electron, so they behave almost the same chemically. Deuterium and tritium are the fuels in the fusion reactions you will meet in Nuclear Fission and Nuclear Fusion.
Worked exampleExample 1: Counting nucleons
Complete the table for these nuclides: (a) ¹⁴₆C (b) ⁶⁰₂₇Co (c) uranium-238 (d) tritium.
- Use Z = protons, A = protons + neutrons, N = A − Z. If only the name is given, look up Z on the periodic table.
- (a) Carbon-14: Z = 6, A = 14, so 6 protons, 8 neutrons.
- (b) Cobalt-60: Z = 27, A = 60, so 27 protons, 33 neutrons.
- (c) Uranium-238: Z = 92, A = 238, so 92 protons, 146 neutrons.
- (d) Tritium is ³₁H: 1 proton, 2 neutrons.
C-14: 6p, 8n. Co-60: 27p, 33n. U-238: 92p, 146n. Tritium: 1p, 2n.
What holds a nucleus together?
Protons are all positive, and like charges repel. Squeezed into a space about 10⁻¹⁵ m across, they push on each other with enormous electric forces. Why doesn't every nucleus fly apart?
A different force, the strong nuclear force, attracts every nucleon to its neighbours, proton to proton, proton to neutron and neutron to neutron. It is much stronger than the electric repulsion, but it acts only over a very short range, about the width of a couple of nucleons.
- In small nuclei, about equal numbers of protons and neutrons are stable (carbon-12 has 6 and 6).
- In bigger nuclei, every proton repels all the other protons, but each nucleon feels the strong force only from its nearest neighbours. So heavy nuclei need extra neutrons, which add strong-force "glue" without adding repulsion. Lead-208 has 82 protons and 126 neutrons.
- If a nucleus has too many or too few neutrons, or is simply too big, it is unstable: it is radioactive and will eventually change into a more stable nucleus. That is the topic of the next lesson, Alpha, Beta and Gamma Radiation.
Worked exampleExample 2: Same element or not?
Which of these are isotopes of the same element? ⁴⁰₁₈Ar, ⁴⁰₂₀Ca, ⁴²₂₀Ca, ³⁹₁₉K
- Isotopes of the same element have the same Z.
- ⁴⁰₂₀Ca and ⁴²₂₀Ca both have Z = 20, so they are isotopes of calcium (20 and 22 neutrons).
- ⁴⁰₁₈Ar and ⁴⁰₂₀Ca have the same mass number but different Z, so they are different elements, not isotopes.
Only calcium-40 and calcium-42 are isotopes of each other.
Canadian scientist: Harriet Brooks
Harriet Brooks (1876–1933), from Ontario, is often called Canada's first woman nuclear physicist. Working with Ernest Rutherford at McGill University in Montréal around 1900, she helped show that radium gives off a radioactive gas (now known as radon), evidence that one element could change into another. Rutherford's team built on this to explain radioactive decay. Brooks did this research at a time when very few women were allowed to work in physics.
Just for funHeavy water really is heavier: it is about 11% denser than ordinary water. An ice cube made of heavy water sinks in a glass of ordinary water instead of floating. (Don't go looking for some; it is not sold at the corner store.)
Hands-on activityBuild a nucleus
You need: two kinds of small objects in different colours (for example two kinds of dried beans, two colours of LEGO bricks or two kinds of cereal), a piece of paper and a pencil. Grown-up note: small objects are a choking hazard for young children; keep them away from little brothers and sisters.
- Decide which object is a proton and which is a neutron. Write a key.
- Build nuclei for protium, deuterium, tritium, helium-4, carbon-12 and carbon-14. For each one, write the nuclear notation, Z, A and N.
- Build lithium-7 (Z = 3). How many neutrons did you need?
- Build two nuclei with the same mass number but different elements (for example ¹⁴₆C and ¹⁴₇N). Explain in a sentence why they are not isotopes.
- Reflection: in your model, what does nothing represent? (Hint: what holds real nucleons together?)
What to look for: correct counts (for example C-14: 6 protons, 8 neutrons; Li-7: 3 protons, 4 neutrons), and the idea that the model leaves out the strong nuclear force, the electrons around the nucleus, and the real scale (a nucleus is about 100 000 times smaller than its atom).
Your turn
1How many protons and neutrons are in ¹⁶₈O?
8 protons, 8 neutrons (16 − 8).
2How many neutrons are in ²³⁵₉₂U?
3Write the nuclear notation for an atom with 26 protons and 30 neutrons (iron).
A = 26 + 30 = 56: ⁵⁶₂₆Fe.
4What is the difference between deuterium and tritium?
Both have 1 proton. Deuterium has 1 neutron and is stable; tritium has 2 neutrons and is radioactive.
5What is heavy water, and where is it used in Canada?
D₂O, water made with deuterium. It is used in CANDU nuclear reactors.
6Why do protons in a nucleus not fly apart from electric repulsion?
The strong nuclear force attracts neighbouring nucleons and, at very short range, it is stronger than the electric repulsion.
7Are ¹²₆C and ¹⁴₆C isotopes? Explain.
Yes. Same Z (6 protons, so both carbon), different mass numbers (6 and 8 neutrons).
More practice: warm-up
The atomic number: the number of protons.
The mass number: protons + neutrons.
3How many neutrons does protium have?
4Write deuterium in nuclear notation.
More practice: on your own
1Complete: cobalt-60 has ___ protons and ___ neutrons (Z for cobalt is 27).
27 protons and 33 neutrons.
2Lead-208 has 82 protons. Compare its numbers of protons and neutrons and explain why it needs that many neutrons.
It has 126 neutrons, many more than protons. In a big nucleus every proton repels all the others, but the strong force only acts between near neighbours, so extra neutrons are needed to add attraction without adding repulsion.
3A nucleus has A = 131 and 78 neutrons. Identify the element (use a periodic table).
Z = 131 − 78 = 53: iodine (iodine-131).
4Why do deuterium and protium have almost identical chemical properties?
Chemistry depends on electrons, and both have one proton and one electron. Only the number of neutrons (and so the mass) differs.
5Give two uses of tritium.
Self-lit exit signs (and similar glowing signs), and fuel for fusion research (D-T fusion).
Challenge
1Natural uranium is about 99.3% U-238 and 0.7% U-235. In a sample of 10 000 uranium atoms, about how many of each are there, and how many more neutrons does each U-238 nucleus have than each U-235 nucleus?
U-238: about 9930 atoms; U-235: about 70 atoms. U-238 has 146 neutrons and U-235 has 143, so 3 more neutrons each.
2The strong nuclear force is stronger than the electric force between protons, yet very large nuclei such as uranium are unstable. Explain.
The strong force has a very short range: each nucleon is attracted only by its nearest neighbours. The electric repulsion has a long range, so each proton is repelled by every other proton in the nucleus. In a very large nucleus, the total repulsion grows faster than the total attraction, so the nucleus becomes unstable.
3A heavy-water molecule is D₂O. Using approximate masses (H = 1 u, D = 2 u, O = 16 u), compare the mass of a D₂O molecule with an H₂O molecule. Why is heavy water about 11% denser rather than exactly this ratio?
H₂O ≈ 18 u, D₂O ≈ 20 u, ratio 20 ÷ 18 ≈ 1.11, about 11% more mass per molecule. Since the molecules are the same size and pack almost the same way, the density is about 11% higher, which matches the measured value well. (Small differences in spacing mean it is close to, not exactly, the mass ratio.)
Quiz
1. What does the atomic number Z tell you?
2. How many neutrons are in ⁵⁶₂₆Fe?
3. Which is the nucleus of tritium?
4. Isotopes of an element have:
6. Why do heavy nuclei have more neutrons than protons?
Big idea: expectation D3.9 asks students to identify and describe the structure of common isotopes, especially hydrogen, deuterium and tritium. This lesson also sets up the vocabulary (Z, A, N, nuclear notation) for decay equations, half-life, fission and fusion.
How to help: Ask your teen to count protons and neutrons for nuclides you pick from a periodic table. The bead or LEGO model is a quick hands-on check.
Common difficulties:
- Confusing A and Z, or subtracting the wrong way (N = A − Z).
- Thinking isotopes are different elements. Same element, different number of neutrons.
- Thinking the decimal atomic mass on the periodic table is the mass number. The periodic-table value is an average over isotopes.
- Believing all isotopes of an element are radioactive, or that none are.
Scientist note: Harriet Brooks is a good example of a Canadian contributor to nuclear physics (A2.2).