B. Matter, Chemical Trends, and Chemical Bonding · Matter, Chemical Trends, and Chemical BondingAtomic Number, Mass Number, Isotopes and Radioisotopes
B3.1 B2.1 A1.12 A2.2About 70 minutes
Learning goals- I can use atomic number and mass number to find the protons, neutrons and electrons in an atom or ion.
- I can write isotopes in isotope notation and hyphen notation.
- I can explain the difference between a stable isotope and a radioisotope.
- I can describe uses and risks of radioisotopes and solve simple half-life problems.
Words to know
atomic number (Z)
The number of protons in the nucleus of an atom. It identifies the element.
mass number (A)
The total number of protons and neutrons in the nucleus.
isotopes
Atoms of the same element (same number of protons) with different numbers of neutrons.
isotope notation
A symbol with the mass number written top left and the atomic number bottom left, e.g. ³⁵₁₇Cl.
radioisotope
An isotope with an unstable nucleus that breaks down and gives off radiation.
half-life
The time it takes for half of the radioactive nuclei in a sample to decay.
ionizing radiation
Radiation with enough energy to knock electrons off atoms; it can damage living cells.
The same element, different weights
In 1951, doctors in Saskatoon and in London, Ontario treated the first cancer patients in the world with a new machine: a cobalt-60 radiation unit. The physicist Harold Johns led the Saskatoon team. Cobalt-60 is still made in Ontario's nuclear reactors and is used around the world to treat cancer and to sterilize medical supplies.
But wait. The cobalt in a steel spoon is not dangerous. So what makes cobalt-60 different? Both are cobalt. Both have 27 protons. The difference is hidden in the nucleus: cobalt-60 has more neutrons than ordinary cobalt, and its nucleus is unstable. In this lesson you will learn to read and write the numbers that describe every atom, and see why some atoms are radioactive.
Remember from Grade 9
In Grade 9 you learned that an atom has a tiny, dense nucleus of protons (+) and neutrons (no charge), surrounded by electrons (−). The atomic number is the number of protons, and the mass number is protons + neutrons. You met isotopes briefly and drew Bohr-Rutherford diagrams. This lesson makes those ideas precise and adds radioactive isotopes.
Atomic number and mass number
Two numbers describe the nucleus of any atom.
- The atomic number (Z) is the number of protons. It decides which element the atom is. Every atom with 6 protons is carbon. Every atom with 17 protons is chlorine. Change the number of protons and you have a different element.
- The mass number (A) is the number of protons + neutrons (together called nucleons). Protons and neutrons each have a mass of about 1 u, and electrons are about 1/1836 as heavy, so almost all of an atom's mass is in its nucleus.
So the number of neutrons is always
neutrons = A − Z
In a neutral atom, the number of electrons equals the number of protons. In an ion, electrons = Z − (charge). For example, Cl⁻ has 17 + 1 = 18 electrons and Mg²⁺ has 12 − 2 = 10 electrons.
Writing isotopes
Isotopes are atoms of the same element (same Z) with different numbers of neutrons (different A). Chemists write them in two ways:
- Isotope notation: the mass number top left and the atomic number bottom left of the symbol, like ³⁵₁₇Cl.
- Hyphen notation: the element name or symbol followed by the mass number, like chlorine-35 or Cl-35.
The atomic number is sometimes left off (³⁵Cl), because the symbol already tells you Z.
Isotopes behave the same in chemical reactions
Chemical reactions involve electrons, not the nucleus. All isotopes of an element have the same number of protons, so their neutral atoms have the same number of electrons and the same electron arrangement. That is why isotopes of an element have nearly identical chemical properties: carbon-12 and carbon-14 both burn to make carbon dioxide.
Isotopes differ in mass and in nuclear stability. Heavier isotopes make slightly denser compounds. For example, heavy water, D₂O (made with hydrogen-2, called deuterium), is about 11% denser than ordinary water. Canada's CANDU nuclear reactors use heavy water to slow down neutrons.
Radioisotopes
Some combinations of protons and neutrons are unstable. Such a nucleus eventually breaks down on its own and gives off radiation, changing into a different nucleus. An isotope with an unstable nucleus is called a radioisotope (radioactive isotope). The three common kinds of radiation are:
- alpha (α) particles: 2 protons + 2 neutrons; stopped by a sheet of paper or skin
- beta (β) particles: fast electrons from the nucleus; stopped by a few millimetres of aluminium
- gamma (γ) rays: high-energy light; need thick lead or concrete to stop
Each radioisotope decays at its own steady rate, described by its half-life: the time it takes for half of the radioactive atoms in a sample to decay. After one half-life, ½ is left; after two, ¼; after three, ⅛; and so on.
| Radioisotope | Half-life (approx.) | Use |
|---|
| cobalt-60 | 5.3 years | cancer radiation therapy; sterilizing medical supplies and some foods |
| technetium-99m | 6 hours | medical imaging (bone and heart scans); short half-life means it is soon gone from the body |
| iodine-131 | 8 days | diagnosing and treating thyroid disease (the thyroid gland collects iodine) |
| carbon-14 | 5730 years | radiocarbon dating of once-living things up to about 50 000 years old |
| americium-241 | 432 years | ionization smoke alarms |
| uranium-235 | 700 million years | fuel in nuclear power reactors |
Benefits and risks
The radiation that makes radioisotopes useful can also harm living things. Radiation from radioisotopes is ionizing: it can knock electrons out of atoms and damage cells and DNA. High doses can cause radiation sickness, and long-term exposure raises the risk of cancer. People who work with radioisotopes (nuclear medicine technologists, radiation therapists, reactor operators) protect themselves with three rules: time (spend as little time near the source as possible), distance (stay far away) and shielding (lead aprons, concrete walls).
The benefits are large too: radiation therapy cures many cancers, and medical scans find disease early. Deciding when to use radioisotopes means weighing risks and benefits, a skill you will practise again at the end of this unit.
Worked exampleExample 1: Counting particles
Find the number of protons, neutrons and electrons in (a) ⁶⁵₃₀Zn, (b) uranium-238, (c) ³²S²⁻.
- (a) Z = 30, so 30 protons. Neutrons = A − Z = 65 − 30 = 35 neutrons. Neutral atom, so 30 electrons.
- (b) The periodic table gives uranium Z = 92: 92 protons. Neutrons = 238 − 92 = 146 neutrons. Neutral: 92 electrons.
- (c) Sulfur has Z = 16: 16 protons. Neutrons = 32 − 16 = 16 neutrons. The charge is 2−, so the ion has gained 2 electrons: 16 + 2 = 18 electrons.
Protons come from Z, neutrons from A − Z, and electrons from Z adjusted for the charge.
Worked exampleExample 2: Same element or not?
Which of these are isotopes of the same element? ⁴⁰₁₈Ar, ⁴⁰₁₉K, ³⁹₁₉K, ⁴⁰₂₀Ca
- Isotopes of one element must have the same atomic number.
- Look at the bottom numbers: 18, 19, 19, 20.
- Only ⁴⁰₁₉K and ³⁹₁₉K share Z = 19 (potassium).
- Notice that ⁴⁰Ar, ⁴⁰K and ⁴⁰Ca all have mass number 40, but they are different elements. Equal mass numbers do not make isotopes.
Potassium-40 and potassium-39 are isotopes. The atoms with mass number 40 are three different elements.
Worked exampleExample 3: Half-life
A hospital receives 120 mg of iodine-131 (half-life 8 days). How much is left after 24 days?
- Number of half-lives = 24 days ÷ 8 days = 3.
- After each half-life, the amount is halved: 120 → 60 → 30 → 15.
- Or in one step: 120 mg × (½)³ = 120 × ⅛ = 15 mg.
15 mg of iodine-131 remains.
Just for funBananas are very slightly radioactive. They are rich in potassium, and about 0.012% of all natural potassium atoms are radioactive potassium-40. The amount is far too small to harm you, and your own body contains potassium-40 too.
Hands-on activityModel isotopes and half-life with coins
You need: about 50 coins (or buttons with a mark on one side), a cup, two kinds of dried beans or cereal pieces, paper and a pencil.
Part 1: build nuclei. Let one kind of bean be protons and the other neutrons. Build nuclei for carbon-12, carbon-13 and carbon-14 (6 protons each; 6, 7 and 8 neutrons). Then build nitrogen-14 (7 protons, 7 neutrons). Which of your nuclei are isotopes of each other? Which two have the same mass number but are different elements? (Answers: the three carbon nuclei are isotopes; carbon-14 and nitrogen-14 share mass number 14 but are different elements.)
Part 2: simulate decay. Each coin is a radioactive atom. Shake all 50 in the cup and spill them. Coins that land heads up have "decayed": remove them. Count and record the coins left. Repeat with the remaining coins until none are left. Each shake is one half-life.
Part 3: graph. Plot coins remaining (y) against shake number (x). Compare your curve with the technetium-99m graph above. You should see about half disappear each shake, but not exactly half: decay is random for single atoms, and only large numbers of atoms follow the half-life rule closely.
What to look for: a curve that drops quickly at first and then levels off, roughly 50, 25, 12, 6, 3, 1.
Your turn
1State the number of protons, neutrons and electrons in ¹⁹₉F.
9 protons, 10 neutrons (19 − 9), 9 electrons.
2Write isotope notation for the atom with 26 protons and 30 neutrons.
Z = 26 is iron; A = 26 + 30 = 56: ⁵⁶₂₆Fe (iron-56).
3How many neutrons are in strontium-90? (Z = 38)
4How many electrons are in Al³⁺? (Z = 13)
5Explain why carbon-12 and carbon-14 have the same chemical properties.
Both have 6 protons, so neutral atoms of each have 6 electrons in the same arrangement. Chemical reactions depend on electrons, so they react the same way.
6A sample of cobalt-60 has a half-life of about 5.3 years. What fraction remains after 10.6 years?
10.6 ÷ 5.3 = 2 half-lives, so ¼ remains.
7Name one medical use and one non-medical use of radioisotopes.
Medical: cobalt-60 radiation therapy, technetium-99m imaging or iodine-131 thyroid treatment. Non-medical: americium-241 in smoke alarms, carbon-14 dating, or uranium-235 reactor fuel. (Any one of each.)
More practice: warm-up
1What does the atomic number tell you?
The number of protons in the nucleus (which decides the element).
2What is the mass number of an atom with 8 protons and 10 neutrons?
3Write chlorine-37 in isotope notation.
4Which kind of radiation is stopped by a sheet of paper?
5True or false: isotopes of the same element have different numbers of protons.
False. They have the same number of protons and different numbers of neutrons.
More practice: on your own
1Complete: an ion has 20 protons, 20 neutrons and 18 electrons. Identify it and write its symbol with the mass number and charge.
Z = 20 is calcium; A = 40; charge = 20 − 18 = +2. ⁴⁰Ca²⁺ (calcium-40 ion).
2An atom has mass number 127 and 74 neutrons. Identify the element.
Z = 127 − 74 = 53, which is iodine (iodine-127).
3Why is technetium-99m a good choice for imaging the inside of the body, but cobalt-60 is not?
Tc-99m has a short half-life (about 6 h), so it gives a useful signal for a scan and is almost gone within a day or two. Cobalt-60 lasts years and gives a strong dose, so it is used only from outside the body in shielded machines.
4A 64 g sample of a radioisotope decays to 4 g in 20 days. What is its half-life?
64 → 32 → 16 → 8 → 4 is 4 half-lives. 20 days ÷ 4 = 5 days.
5Heavy water (D₂O) and ordinary water (H₂O) both freeze and react with sodium. Use the idea of isotopes to explain why they are so similar, and name one property that differs.
Deuterium and hydrogen are isotopes: same protons and electrons, so the same chemistry. They differ in mass, so D₂O is denser (about 11% denser) than H₂O.
Challenge
1An ion has 35 protons, 46 neutrons and a charge of 1−. Give its mass number, its number of electrons and its full symbol.
A = 35 + 46 = 81; electrons = 35 + 1 = 36; Z = 35 is bromine: ⁸¹₃₅Br⁻.
2Carbon-14 has a half-life of 5730 years. A piece of wood has ⅛ of the carbon-14 found in a living tree. About how old is it? Why would carbon-14 dating not work for a 10-million-year-old fossil?
⅛ = (½)³, so 3 half-lives: 3 × 5730 = 17 190 years (about 17 000 years). After 10 million years, about 1745 half-lives have passed, so practically no carbon-14 is left to measure.
3Argon-40 and calcium-40 have the same mass number. Explain why they are not isotopes, and give the number of neutrons in each.
Isotopes must be the same element (same Z). Argon has Z = 18 and calcium Z = 20, so they are different elements. Neutrons: Ar-40 has 40 − 18 = 22; Ca-40 has 40 − 20 = 20.
Quiz
1. How many neutrons are in ¹³⁷₅₅Cs?
2. Which pair are isotopes of the same element?
3. What is the number of electrons in N³⁻ (Z = 7)?
4. Isotopes of the same element have nearly identical chemical properties because they have the same
5. A radioisotope has a half-life of 3 days. What fraction of a sample remains after 9 days?
6. Which radioisotope is used in ionization smoke alarms?
Big idea: Expectation B3.1 asks students to explain how atomic number and mass number relate, and the difference between isotopes and radioisotopes, including how radioisotopes are used and their risks.
How to help: Ask your teen to "read" isotope symbols aloud: "chlorine-37 has 17 protons, 20 neutrons, 17 electrons." Flip the coin simulation together and graph it; it makes half-life concrete. A smoke alarm label (many say they contain americium-241) is a good real-world link; do not open the alarm.
Common difficulties:
- Mixing up atomic number and mass number. Atomic number is the smaller number (protons only).
- Thinking isotopes have different numbers of protons, or that atoms with the same mass number are isotopes.
- Forgetting to adjust electrons for an ion's charge: negative ions have more electrons than protons.
- Thinking a sample is gone after two half-lives. Each half-life halves what is left: ½, ¼, ⅛...
A note on worry: some teens feel anxious about radiation. Reassure them that background radiation is natural and that radioisotopes in medicine and smoke alarms are tightly regulated in Canada by the Canadian Nuclear Safety Commission.