Basic ideas about atoms

What you'll learn

How radioactive decay changes atomic number and mass number, including positron emission and electron capture.
How α, β and γ radiation behave, how half-life works, and why radioisotopes are useful but risky.
How ionisation energies reveal electronic structure.
How orbitals, electron configurations and atomic spectra link to quantised electron energy levels.

1. Atoms, nuclei and why models matter

An atom has a tiny, positively charged nucleus containing protons and neutrons, with electrons arranged around it in energy levels. Different models of the atom explain different evidence: the nuclear model explains radioactivity, while shells and orbitals help explain ionisation energies and spectra.

Scientific models are not “guesses”; they are evidence-based explanations that improve over time as new observations are made.

Definition

Atomic number and mass number

Atomic number, $Z$ , is the number of protons in the nucleus.
Mass number, $A$ , is the total number of protons and neutrons.
Isotopes are atoms of the same element with the same $Z$ but different $A$ .
A radioisotope is an isotope with an unstable nucleus that undergoes radioactive decay.

2. Radioactive decay

Definition

Radioactive decay

Radioactive decay is the spontaneous, random change of an unstable nucleus into a more stable nucleus, with emission of radiation.

“Random” means you cannot predict exactly when one nucleus will decay. However, with a very large number of nuclei, you can predict the overall rate statistically.

Types of nuclear decay

In nuclear equations, the total mass number and total atomic number must balance.

Alpha emission:

ZAX→Z−2A−4Y+24He{}^{A}_{Z}\text{X} \to {}^{A-4}_{Z-2}\text{Y} + {}^{4}_{2}\text{He}

Beta-minus emission:

ZAX→Z+1AY+−10e{}^{A}_{Z}\text{X} \to {}^{A}_{Z+1}\text{Y} + {}^{0}_{-1}\text{e}

Positron emission:

ZAX→Z−1AY++10e{}^{A}_{Z}\text{X} \to {}^{A}_{Z-1}\text{Y} + {}^{0}_{+1}\text{e}

Electron capture:

ZAX+−10e→Z−1AY{}^{A}_{Z}\text{X} + {}^{0}_{-1}\text{e} \to {}^{A}_{Z-1}\text{Y}

Gamma emission releases energy only, so $A$ and $Z$ are unchanged.

Radioactive emissions, deflection in electric fields and penetration through materials

Example

Balancing an electron-capture equation

Complete the equation for electron capture by potassium-40.

In electron capture, an inner electron is captured by the nucleus, so the electron appears on the left-hand side:

{}^{40}_{19}\text{K} + {}^{0}_{-1}\text{e} \to {}^{A}_{Z}\text{Y}

Balance mass numbers:

40 + 0 = A

so $A = 40$ .

Balance atomic numbers:

19 + (- 1) = Z

so $Z = 18$ .

Atomic number 18 is argon, so:

{}^{40}_{19}\text{K} + {}^{0}_{-1}\text{e} \to {}^{40}_{18}\text{Ar}

Common Mistake

Beta decay and mass number

In beta-minus, beta-plus and electron capture processes, the mass number does not change. The particle involved has mass number 0, so only the atomic number changes.

3. Alpha, beta and gamma radiation

Alpha, beta and gamma radiation differ in charge, mass, ionising power and penetrating power.

Alpha radiation is made of helium nuclei, $24He{}^{4}_{2}\text{He}$ . It has charge +2, is strongly ionising, but is stopped by paper or skin.
Beta-minus radiation is made of fast electrons. It has charge −1, is moderately penetrating, and is stopped by a few millimetres of aluminium.
Beta-plus radiation is made of positrons. A positron has the same mass as an electron but charge +1.
Gamma radiation is high-energy electromagnetic radiation. It has no mass or charge, is weakly ionising per collision, but is very penetrating and needs thick lead or concrete to reduce it.

In an electric field, charged radiation is deflected: positive particles bend towards the negative plate, negative particles bend towards the positive plate, and gamma radiation is not deflected. In a magnetic field, alpha and beta radiation are also deflected in opposite directions; gamma is unaffected.

4. Half-life

Definition

Half-life

The half-life of a radioisotope is the time taken for half the unstable nuclei in a sample to decay, or for the corrected count rate to fall to half its initial value.

Half-life is not affected by temperature, pressure or chemical state. It is a nuclear property, not a chemical one.

Common Mistake

Background radiation

A detector records background radiation as well as radiation from the sample. In half-life calculations using count rate, subtract the background count rate before using ratios.

Example

Using half-life with count rate

A radioactive sample has a measured count rate of 820 counts min⁻¹. The background count rate is 20 counts min⁻¹. Later, the measured count rate is 70 counts min⁻¹. The half-life is 6.0 h. Find the time elapsed.

Correct both count rates by subtracting background:
initial corrected count rate = 820 − 20 = 800 counts min⁻¹
later corrected count rate = 70 − 20 = 50 counts min⁻¹
Find the ratio:

\frac{800}{50} = 16

Since $16 = 2^4$ , four half-lives have passed.

Calculate the time:

\times 6.0\ \text{h} = 24\ \text{h}

5. Radiation: risks and uses

Ionising radiation can remove electrons from atoms and molecules in living cells. This can damage DNA and proteins, causing mutations, cancer, burns or cell death. Risk depends on dose, exposure time, radiation type and whether the source is outside or inside the body.

Key Idea

Benefit versus risk

Radioisotopes are useful because their radiation is detectable and their decay is predictable, but their use must be justified by benefit, minimised dose, shielding, distance, exposure-time control and safe disposal.

Important uses include:

Medicine: technetium-99m for diagnostic imaging; iodine-131 for thyroid treatment; cobalt-60 for radiotherapy or sterilising equipment.
Health and biological analysis: tracers can follow movement of substances through organs or biochemical pathways.
Radio-dating: carbon-14 dating estimates the age of once-living material using known half-life.
Industry: thickness gauges, leak detection in pipes and checking material integrity.
Analysis: emitted radiation can help identify trace elements, for example in neutron activation analysis.

Ethically, you should weigh diagnostic or industrial benefit against radiation dose, consent, worker safety, environmental contamination and radioactive waste.

6. Ionisation energy and electronic structure

Definition

First ionisation energy

The first standard molar ionisation energy is the enthalpy change when one mole of gaseous atoms each loses one electron to form one mole of gaseous 1+ ions.

X(g)→X+(g)+e−\text{X(g)} \to \text{X}^{+}\text{(g)} + \text{e}^{-}

Ionisation energies are positive because energy is needed to remove an electron attracted to the nucleus.

Across a period, first ionisation energy generally increases because nuclear charge increases while shielding changes only slightly. Down a group, it generally decreases because the outer electron is farther from the nucleus and more shielded.

Successive ionisation energies always increase, but a large jump shows that the next electron is being removed from an inner shell. This reveals the number of electrons in the outer shell.

Example

Using successive ionisation energies

An element has successive ionisation energies of 738, 1451, 7733 and 10543 kJ mol⁻¹. Deduce the group.

Compare the increases between values. The biggest jump is between the second and third ionisation energies: from 1451 to 7733 kJ mol⁻¹.
The first two electrons are removed relatively easily, but the third is much harder to remove because it is from an inner shell.
Therefore the atom has two outer-shell electrons, so it is in Group 2.

7. Orbitals and electron configurations

Definition

Atomic orbital

An atomic orbital is a region around the nucleus that can hold up to two electrons with opposite spins.

Electrons occupy shells, labelled by principal quantum number $n$ , and sub-shells, labelled s, p and d.

An s sub-shell contains one orbital, so it holds 2 electrons.
A p sub-shell contains three orbitals, so it holds 6 electrons.
A d sub-shell contains five orbitals, so it holds 10 electrons.

An s orbital is spherical. A p orbital is dumbbell-shaped, with three orientations: $p_x$ , $p_y$ and $p_z$ .

For elements 1–36, the usual filling order is:

4p1s,\ 2s,\ 2p,\ 3s,\ 3p,\ 4s,\ 3d,\ 4p

s and p orbital shapes with orbital filling order up to element 36

Example

Writing an electron configuration

Write the electron configuration of bromine, atomic number 35.

A neutral bromine atom has 35 electrons, because it has 35 protons.
Fill sub-shells in order up to argon, which accounts for 18 electrons:

1s^2\,2s^2\,2p^6\,3s^2\,3p^6

Continue using the filling order: add $4s^2$ to reach 20 electrons, then $3d^{10}$ to reach 30 electrons.
Put the remaining 5 electrons in $4 p$ :

1s^2\,2s^2\,2p^6\,3s^2\,3p^6\,4s^2\,3d^{10}\,4p^5

Common Mistake

Chromium and copper

For neutral atoms, chromium is $4s1\text{[Ar] }3d^5\,4s^1$ and copper is $4s1\text{[Ar] }3d^{10}\,4s^1$ , rather than the simple predicted arrangements. Half-filled and full d sub-shells are especially stable.

8. Spectra, photons and electron transitions

Atoms only allow electrons to have certain energies. These are quantised energy levels.

Definition

Line spectrum

A line spectrum is a pattern of separate wavelengths of light emitted or absorbed by atoms, caused by electron transitions between quantised energy levels.

In an emission spectrum, an electron falls from a higher energy level to a lower one and emits a photon. In an absorption spectrum, an electron absorbs a photon and moves to a higher energy level.

The photon energy equals the energy gap:

E = h f

where $E$ is energy, $h$ is the Planck constant and $f$ is frequency. Frequency and wavelength are related by:

\frac{c}{\lambda}

where $c$ is the speed of light and $λ\lambda$ is wavelength.

Increasing energy order is:

Einfrared<Evisible<EultravioletE_\text{infrared} < E_\text{visible} < E_\text{ultraviolet}

So ultraviolet has higher frequency and shorter wavelength than visible light; infrared has lower frequency and longer wavelength.

Hydrogen emission spectrum and the Lyman limit

Hydrogen has one electron, so its spectrum is especially important evidence for quantised energy levels. Transitions down to $n = 1$ form the Lyman series, which is in the ultraviolet. Transitions down to $n = 2$ form the Balmer series, much of which is visible.

The lines in a series get closer together and converge. The Lyman convergence limit corresponds to an electron falling from $\infty$ to $n = 1$ . Its frequency is linked to the ionisation energy of hydrogen from the ground state:

IEH=hflimitNAIE_\text{H} = h f_\text{limit} N_A

Hydrogen energy levels, Lyman and Balmer series, and convergence limit

Example

Calculating hydrogen ionisation energy from the Lyman limit

The Lyman convergence limit has wavelength 91.2 nm. Calculate the molar ionisation energy of hydrogen. Use $\times 10^{-34}\ \text{J s}$ , $\times 10^8\ \text{m s}^{-1}$ and $mol−1N_A = 6.022 \times 10^{23}\ \text{mol}^{-1}$ .

Convert wavelength into metres:

91.2\ \text{nm} = 91.2 \times 10^{-9}\ \text{m}

Calculate frequency:

\frac{c}{\lambda} = \frac{3.00 \times 10^8}{91.2 \times 10^{-9}} = 3.29 \times 10^{15}\ \text{s}^{-1}

Calculate energy per atom:

\times 10^{-34})(3.29 \times 10^{15}) = 2.18 \times 10^{-18}\ \text{J}

Convert to molar ionisation energy:

\times 10^{-18})(6.022 \times 10^{23}) = 1.31 \times 10^6\ \text{J mol}^{-1}

1310\ \text{kJ mol}^{-1}

Exam technique

In the exam

For nuclear equations, balance mass number and atomic number separately; remember that electron capture puts an electron on the reactant side.
For half-life questions, subtract background count rate first, then use powers of two or repeated halving.
For ionisation energy and spectra calculations, watch units carefully: nm to m, J mol⁻¹ to kJ mol⁻¹, and identify big jumps or convergence limits.

Self review

Check yourself

A nuclide emits a positron. What happens to its mass number and atomic number?
A set of successive ionisation energies has a large jump after the fifth electron is removed. What does that tell you about the outer shell?
How would you use the Lyman convergence limit to calculate the ionisation energy of hydrogen?

What you'll learn

How radioactive decay changes atomic number and mass number, including positron emission and electron capture.
How α, β and γ radiation behave, how half-life works, and why radioisotopes are useful but risky.
How ionisation energies reveal electronic structure.
How orbitals, electron configurations and atomic spectra link to quantised electron energy levels.

1. Atoms, nuclei and why models matter

Scientific models are not “guesses”; they are evidence-based explanations that improve over time as new observations are made.

Definition

Atomic number and mass number

Atomic number, $Z$ , is the number of protons in the nucleus.
Mass number, $A$ , is the total number of protons and neutrons.
Isotopes are atoms of the same element with the same $Z$ but different $A$ .
A radioisotope is an isotope with an unstable nucleus that undergoes radioactive decay.

2. Radioactive decay

Definition

Radioactive decay

Radioactive decay is the spontaneous, random change of an unstable nucleus into a more stable nucleus, with emission of radiation.

“Random” means you cannot predict exactly when one nucleus will decay. However, with a very large number of nuclei, you can predict the overall rate statistically.

Types of nuclear decay

In nuclear equations, the total mass number and total atomic number must balance.

Alpha emission:

ZAX→Z−2A−4Y+24He{}^{A}_{Z}\text{X} \to {}^{A-4}_{Z-2}\text{Y} + {}^{4}_{2}\text{He}

Beta-minus emission:

ZAX→Z+1AY+−10e{}^{A}_{Z}\text{X} \to {}^{A}_{Z+1}\text{Y} + {}^{0}_{-1}\text{e}

Positron emission:

ZAX→Z−1AY++10e{}^{A}_{Z}\text{X} \to {}^{A}_{Z-1}\text{Y} + {}^{0}_{+1}\text{e}

Electron capture:

ZAX+−10e→Z−1AY{}^{A}_{Z}\text{X} + {}^{0}_{-1}\text{e} \to {}^{A}_{Z-1}\text{Y}

Gamma emission releases energy only, so $A$ and $Z$ are unchanged.

Radioactive emissions, deflection in electric fields and penetration through materials

Example

Balancing an electron-capture equation

Complete the equation for electron capture by potassium-40.

In electron capture, an inner electron is captured by the nucleus, so the electron appears on the left-hand side:

{}^{40}_{19}\text{K} + {}^{0}_{-1}\text{e} \to {}^{A}_{Z}\text{Y}

Balance mass numbers:

40 + 0 = A

so $A = 40$ .

Balance atomic numbers:

19 + (- 1) = Z

so $Z = 18$ .

Atomic number 18 is argon, so:

{}^{40}_{19}\text{K} + {}^{0}_{-1}\text{e} \to {}^{40}_{18}\text{Ar}

Common Mistake

Beta decay and mass number

In beta-minus, beta-plus and electron capture processes, the mass number does not change. The particle involved has mass number 0, so only the atomic number changes.

3. Alpha, beta and gamma radiation

Alpha, beta and gamma radiation differ in charge, mass, ionising power and penetrating power.

Alpha radiation is made of helium nuclei, $24He{}^{4}_{2}\text{He}$ . It has charge +2, is strongly ionising, but is stopped by paper or skin.
Beta-minus radiation is made of fast electrons. It has charge −1, is moderately penetrating, and is stopped by a few millimetres of aluminium.
Beta-plus radiation is made of positrons. A positron has the same mass as an electron but charge +1.
Gamma radiation is high-energy electromagnetic radiation. It has no mass or charge, is weakly ionising per collision, but is very penetrating and needs thick lead or concrete to reduce it.

4. Half-life

Definition

Half-life

The half-life of a radioisotope is the time taken for half the unstable nuclei in a sample to decay, or for the corrected count rate to fall to half its initial value.

Half-life is not affected by temperature, pressure or chemical state. It is a nuclear property, not a chemical one.

Common Mistake

Background radiation

A detector records background radiation as well as radiation from the sample. In half-life calculations using count rate, subtract the background count rate before using ratios.

Example

Using half-life with count rate

Correct both count rates by subtracting background:
initial corrected count rate = 820 − 20 = 800 counts min⁻¹
later corrected count rate = 70 − 20 = 50 counts min⁻¹
Find the ratio:

\frac{800}{50} = 16

Since $16 = 2^4$ , four half-lives have passed.

Calculate the time:

\times 6.0\ \text{h} = 24\ \text{h}

5. Radiation: risks and uses

Key Idea

Benefit versus risk

Important uses include:

Medicine: technetium-99m for diagnostic imaging; iodine-131 for thyroid treatment; cobalt-60 for radiotherapy or sterilising equipment.
Health and biological analysis: tracers can follow movement of substances through organs or biochemical pathways.
Radio-dating: carbon-14 dating estimates the age of once-living material using known half-life.
Industry: thickness gauges, leak detection in pipes and checking material integrity.
Analysis: emitted radiation can help identify trace elements, for example in neutron activation analysis.

Ethically, you should weigh diagnostic or industrial benefit against radiation dose, consent, worker safety, environmental contamination and radioactive waste.

6. Ionisation energy and electronic structure

Definition

First ionisation energy

The first standard molar ionisation energy is the enthalpy change when one mole of gaseous atoms each loses one electron to form one mole of gaseous 1+ ions.

X(g)→X+(g)+e−\text{X(g)} \to \text{X}^{+}\text{(g)} + \text{e}^{-}

Ionisation energies are positive because energy is needed to remove an electron attracted to the nucleus.

Successive ionisation energies always increase, but a large jump shows that the next electron is being removed from an inner shell. This reveals the number of electrons in the outer shell.

Example

Using successive ionisation energies

An element has successive ionisation energies of 738, 1451, 7733 and 10543 kJ mol⁻¹. Deduce the group.

Compare the increases between values. The biggest jump is between the second and third ionisation energies: from 1451 to 7733 kJ mol⁻¹.
The first two electrons are removed relatively easily, but the third is much harder to remove because it is from an inner shell.
Therefore the atom has two outer-shell electrons, so it is in Group 2.

7. Orbitals and electron configurations

Definition

Atomic orbital

An atomic orbital is a region around the nucleus that can hold up to two electrons with opposite spins.

Electrons occupy shells, labelled by principal quantum number $n$ , and sub-shells, labelled s, p and d.

An s sub-shell contains one orbital, so it holds 2 electrons.
A p sub-shell contains three orbitals, so it holds 6 electrons.
A d sub-shell contains five orbitals, so it holds 10 electrons.

An s orbital is spherical. A p orbital is dumbbell-shaped, with three orientations: $p_x$ , $p_y$ and $p_z$ .

For elements 1–36, the usual filling order is:

4p1s,\ 2s,\ 2p,\ 3s,\ 3p,\ 4s,\ 3d,\ 4p

s and p orbital shapes with orbital filling order up to element 36

Example

Writing an electron configuration

Write the electron configuration of bromine, atomic number 35.

A neutral bromine atom has 35 electrons, because it has 35 protons.
Fill sub-shells in order up to argon, which accounts for 18 electrons:

1s^2\,2s^2\,2p^6\,3s^2\,3p^6

Continue using the filling order: add $4s^2$ to reach 20 electrons, then $3d^{10}$ to reach 30 electrons.
Put the remaining 5 electrons in $4 p$ :

1s^2\,2s^2\,2p^6\,3s^2\,3p^6\,4s^2\,3d^{10}\,4p^5

Common Mistake

Chromium and copper

8. Spectra, photons and electron transitions

Atoms only allow electrons to have certain energies. These are quantised energy levels.

Definition

Line spectrum

A line spectrum is a pattern of separate wavelengths of light emitted or absorbed by atoms, caused by electron transitions between quantised energy levels.

The photon energy equals the energy gap:

E = h f

where $E$ is energy, $h$ is the Planck constant and $f$ is frequency. Frequency and wavelength are related by:

\frac{c}{\lambda}

where $c$ is the speed of light and $λ\lambda$ is wavelength.

Increasing energy order is:

Einfrared<Evisible<EultravioletE_\text{infrared} < E_\text{visible} < E_\text{ultraviolet}

So ultraviolet has higher frequency and shorter wavelength than visible light; infrared has lower frequency and longer wavelength.

Hydrogen emission spectrum and the Lyman limit

IEH=hflimitNAIE_\text{H} = h f_\text{limit} N_A

Hydrogen energy levels, Lyman and Balmer series, and convergence limit

Example

Calculating hydrogen ionisation energy from the Lyman limit

Convert wavelength into metres:

91.2\ \text{nm} = 91.2 \times 10^{-9}\ \text{m}

Calculate frequency:

\frac{c}{\lambda} = \frac{3.00 \times 10^8}{91.2 \times 10^{-9}} = 3.29 \times 10^{15}\ \text{s}^{-1}

Calculate energy per atom:

\times 10^{-34})(3.29 \times 10^{15}) = 2.18 \times 10^{-18}\ \text{J}

Convert to molar ionisation energy:

\times 10^{-18})(6.022 \times 10^{23}) = 1.31 \times 10^6\ \text{J mol}^{-1}

1310\ \text{kJ mol}^{-1}

Exam technique

In the exam

For nuclear equations, balance mass number and atomic number separately; remember that electron capture puts an electron on the reactant side.
For half-life questions, subtract background count rate first, then use powers of two or repeated halving.
For ionisation energy and spectra calculations, watch units carefully: nm to m, J mol⁻¹ to kJ mol⁻¹, and identify big jumps or convergence limits.

Self review

Check yourself

A nuclide emits a positron. What happens to its mass number and atomic number?
A set of successive ionisation energies has a large jump after the fifth electron is removed. What does that tell you about the outer shell?
How would you use the Lyman convergence limit to calculate the ionisation energy of hydrogen?

What you'll learn

1. Atoms, nuclei and why models matter

2. Radioactive decay

Types of nuclear decay

3. Alpha, beta and gamma radiation

4. Half-life

5. Radiation: risks and uses

6. Ionisation energy and electronic structure

7. Orbitals and electron configurations

8. Spectra, photons and electron transitions

Hydrogen emission spectrum and the Lyman limit

Review Basic ideas about atoms by teaching Genie

Recap your knowledge with an interactive lesson

Remember key concepts with flashcards

Basic ideas about atoms

What you'll learn

1. Atoms, nuclei and why models matter

2. Radioactive decay

Types of nuclear decay

3. Alpha, beta and gamma radiation

4. Half-life

5. Radiation: risks and uses

6. Ionisation energy and electronic structure

7. Orbitals and electron configurations

8. Spectra, photons and electron transitions

Hydrogen emission spectrum and the Lyman limit

Review Basic ideas about atoms by teaching Genie

Recap your knowledge with an interactive lesson

Remember key concepts with flashcards

Basic ideas about atoms

What you'll learn

1. Atoms, nuclei and why models matter

2. Radioactive decay

Types of nuclear decay

3. Alpha, beta and gamma radiation

4. Half-life

5. Radiation: risks and uses

6. Ionisation energy and electronic structure

7. Orbitals and electron configurations

8. Spectra, photons and electron transitions

Hydrogen emission spectrum and the Lyman limit

Review Basic ideas about atoms by teaching Genie

Recap your knowledge with an interactive lesson

Remember key concepts with flashcards

Basic ideas about atoms Revision Guide

Basic ideas about atoms

What you'll learn

1. Atoms, nuclei and why models matter

2. Radioactive decay

Types of nuclear decay

3. Alpha, beta and gamma radiation

4. Half-life

5. Radiation: risks and uses

6. Ionisation energy and electronic structure

7. Orbitals and electron configurations

8. Spectra, photons and electron transitions

Hydrogen emission spectrum and the Lyman limit

Review Basic ideas about atoms by teaching Genie

Recap your knowledge with an interactive lesson

Remember key concepts with flashcards

Basic ideas about atoms Revision Guide