Atomic spectra, ionisation energies and fusion

Q: What is nuclear fusion, and why does it require extremely high temperatures and pressures?

Nuclear fusion is the process where two light atomic nuclei collide and merge to form a heavier nucleus. Extremely high temperatures and pressures are required to provide sufficient kinetic energy and collision frequency to overcome the strong electrostatic repulsion between positively charged nuclei.

Q: What two conservation laws must be satisfied when writing and balancing nuclear equations?

The sum of the mass numbers (nucleons, top numbers) and the sum of the atomic numbers (proton charges, bottom numbers) must be equal on both sides of the equation.

Q: What is the difference between an atomic emission spectrum and an atomic absorption spectrum?

An emission spectrum consists of coloured lines on a dark background produced when excited electrons drop to lower energy levels and release photons, whereas an absorption spectrum consists of dark lines on a continuous background produced when ground-state electrons absorb specific frequencies of light to reach higher energy levels.

Q: What experimental evidence indicates that electron energy levels in an atom are quantised?

The appearance of discrete line spectra rather than a continuous spectrum provides evidence that electrons can only occupy specific, fixed energy levels.

Q: What causes spectral lines to converge in a series, and what does the convergence limit represent?

Lines converge because the energy levels get closer together as the principal quantum number \(n\) increases; the convergence limit represents the electron reaching \(n = \infty\), where it is completely removed from the nucleus (ionisation).

Q: What is the definition of first ionisation energy?

The first ionisation energy is the energy required to remove one electron from each atom in one mole of gaseous atoms to form one mole of gaseous \(1+\) ions.

Q: Why do successive ionisation energies always increase for any given element?

Successive electrons are being removed from an increasingly positive ion, which exerts a stronger electrostatic pull on the remaining electrons due to an increased proton-to-electron ratio.

Q: What three main factors determine the magnitude of an ionisation energy?

Nuclear charge (number of protons), atomic radius (distance from nucleus), and shielding (screening by inner electron shells).

Q: How do successive ionisation energies provide direct evidence for the existence of electron shells?

A large, sudden jump in successive ionisation energies indicates that an electron is being removed from a new inner shell that is closer to the nucleus with less shielding.

Q: How is the first ionisation energy of hydrogen calculated from the convergence limit of the Lyman series?

By calculating the energy of a single photon at the convergence frequency using \(\Delta E = h\nu_{\text{limit}}\) and multiplying by the Avogadro constant \(N_{\text{A}}\) to obtain the molar energy.

Chemistry B (Salters) - H433 · Cambridge OCR A Level · 10 min read · Updated: 22 Oct 2026

Introduction: Unlocking the Secrets of the Atom

Welcome to this guide on atomic spectra, ionisation energies, and nuclear fusion! In the OCR Chemistry B (Salters) course, these ideas are introduced in the Elements of life storyline. Have you ever wondered where the chemical elements that make up your body, your smartphone, and the world around you actually came from? Or how scientists worked out that electrons sit in fixed energy levels around a nucleus without ever seeing one directly?

In this chapter, we will connect the physics of the stars to the arrangement of electrons in atoms. We will explore how lighter nuclei fuse under extreme stellar conditions to build heavier elements, how atoms absorb and emit distinct lines of light, and how measuring the energy required to remove electrons provides indisputable evidence for atomic electron shells.

Note: Detailed subshell configurations and periodic trends across rows and down groups are developed further in our companion chapters on "Atomic structure and electron configurations" and "Periodicity and the periodic table".

1. Nuclear Fusion: The Stellar Origin of Elements

Every element heavier than hydrogen was forged inside stars through processes called nuclear fusion. Nuclear fusion occurs when two light atomic nuclei collide with enough energy to overcome their mutual electrostatic repulsion and merge to form a single, heavier nucleus.

The Electrostatic Barrier

Atomic nuclei carry a positive electric charge because they contain protons. Under everyday conditions on Earth, positive charges strongly repel each other (like charges repel). For two nuclei to fuse, they must get close enough for the short-range strong nuclear attraction to take over. To overcome this enormous electrostatic repulsion:

• Extremely high temperatures are required to give the nuclei immense kinetic energy, allowing them to move at tremendous speeds.

• Extremely high pressures and densities are required to ensure a sufficiently high collision frequency between nuclei.

These intense conditions exist naturally in the cores of stars, such as our Sun, where hydrogen nuclei fuse to form helium.

Writing and Balancing Nuclear Equations

Nuclear equations are balanced differently from ordinary chemical equations. In a nuclear reaction, elements can change identity! However, two fundamental rules must always be obeyed:

1. Conservation of Mass Number: The sum of the mass numbers (top numbers, nucleons) on the left-hand side must equal the sum on the right-hand side.

2. Conservation of Atomic Number: The sum of the atomic numbers (bottom numbers, proton charges) on the left-hand side must equal the sum on the right-hand side.

For example, inside a star, deuterium (\(^{2}_{1}\text{H}\)) can fuse with tritium (\(^{3}_{1}\text{H}\)) to produce helium and release a high-energy neutron:

\(^{2}_{1}\text{H} + {^{3}_{1}\text{H}} \rightarrow {^{4}_{2}\text{He}} + {^{1}_{0}\text{n}}\)

Let's check the balance:

• Top (mass numbers): \(2 + 3 = 5\) on the left; \(4 + 1 = 5\) on the right. Balanced!

• Bottom (atomic numbers): \(1 + 1 = 2\) on the left; \(2 + 0 = 2\) on the right. Balanced!

Quick Review & Key Takeaway: Nuclear fusion builds heavier elements from lighter ones. It requires extreme temperatures and pressures to overcome the electrostatic repulsion between positively charged nuclei.

2. Atomic Spectra and Quantised Energy Levels

How do we know what stars are made of, and how do we know how electrons are arranged in atoms? The answer comes from atomic spectroscopy.

Continuous Spectra vs. Line Spectra

White light from a tungsten bulb or the sun passes through a prism to give a continuous spectrum containing all wavelengths/frequencies of visible light with no gaps. However, when gaseous atoms are excited, they produce a line spectrum composed of sharp, discrete coloured lines on a dark background.

• Emission spectra: When an electric discharge or intense heat is passed through a gas, electrons absorb energy and are promoted to higher energy levels (the excited state). As they drop back down to lower energy levels (the ground state), they release photons of light of specific energies: \(\Delta E = h\nu\). When focused through a spectrometer, this emits discrete bright lines.

• Absorption spectra: When continuous white light is shone through cold gaseous atoms, the atoms absorb specific frequencies of light corresponding precisely to the energy jumps needed to excite electrons upwards. The resulting spectrum shows dark lines at exactly the same frequencies as the emission spectrum.

Quantised Energy Levels and the Hydrogen Spectrum

Because the spectrum consists of discrete lines rather than a continuous smear of colours, the energy levels within the atom must be quantised. This means electrons can only exist in certain fixed energy levels, never in-between.

In the hydrogen atom, when excited electrons drop down to different levels, distinct series of spectral lines are observed:

• Lyman series: Electron transitions falling down to the ground state, \(n = 1\). Because these transitions involve the largest energy gaps, the emitted radiation has high frequency and falls in the ultraviolet (UV) region.

• Balmer series: Electron transitions falling down to \(n = 2\). These transitions involve intermediate energy gaps, falling in the visible region.

• Paschen series: Electron transitions falling down to \(n = 3\). These involve smaller energy gaps, falling in the infrared (IR) region.

Convergence and the Convergence Limit

If you look at the lines in any one series (such as the Lyman series), you will notice that as the frequency increases, the lines get closer and closer together until they merge. This point is called the convergence limit.

Why do the lines converge? The energy levels in an atom become increasingly closer together the further away they are from the nucleus (as \(n\) increases). At the convergence limit, the electron reaches \(n = \infty\), which means it has absorbed enough energy to be completely removed from the influence of the nucleus. The atom has been ionised!

Key Formulae for Calculations:

• Frequency and energy: \(\Delta E = h\nu\)

• Wave equation: \(c = \nu\lambda\)

Where:

• \(\Delta E\) is the energy difference in joules (\(\text{J}\))

• \(h\) is the Planck constant (\(6.63 \times 10^{-34}\text{ J Hz}^{-1}\) as provided on the Salters Data Sheet)

• \(\nu\) is frequency in hertz (\(\text{Hz}\) or \(\text{s}^{-1}\))

• \(c\) is the speed of light in a vacuum (\(3.00 \times 10^8\text{ m s}^{-1}\))

• \(\lambda\) is wavelength in metres (\(\text{m}\))

Quick Review & Key Takeaway: Atomic line spectra provide experimental evidence that electron energy levels are quantised. The convergence limit of the Lyman series corresponds to the energy needed to remove an electron completely from the \(n = 1\) level of a hydrogen atom to infinity.

3. Ionisation Energies: Evidence for Atomic Structure

Ionisation energy data offers direct experimental proof of the electron shell arrangements inside atoms.

Definition of First Ionisation Energy

The first ionisation energy (\(\Delta H_{\text{i1}}\)) is the energy required to remove one electron from each atom in one mole of gaseous atoms to form one mole of gaseous \(1+\) ions.

You must always include the correct gas state symbols \(\text{(g)}\) in the equation:

\(\text{X(g)} \rightarrow \text{X}^+\text{(g)} + \text{e}^-\)

For example, for magnesium:

\(\text{Mg(g)} \rightarrow \text{Mg}^+\text{(g)} + \text{e}^-\)

Successive Ionisation Energies

You can continue to strip electrons away one after another. These are known as successive ionisation energies:

• Second ionisation energy: \(\text{X}^+\text{(g)} \rightarrow \text{X}^{2+}\text{(g)} + \text{e}^-\)

• Third ionisation energy: \(\text{X}^{2+}\text{(g)} \rightarrow \text{X}^{3+}\text{(g)} + \text{e}^-\)

• General \(n\)-th ionisation energy: \(\text{X}^{(n-1)+}\text{(g)} \rightarrow \text{X}^{n+}\text{(g)} + \text{e}^-\)

Important Rule: Successive ionisation energies always increase (\(\text{IE}_1 < \text{IE}_2 < \text{IE}_3 < \dots\)). This is because each subsequent electron is being removed from an increasingly positive ion. The ratio of positive protons to negative electrons increases, pulling the remaining electrons closer to the nucleus and increasing the electrostatic attraction.

The Three Deciding Factors

The magnitude of any ionisation energy depends on the net balance of three factors:

1. Nuclear Charge: More protons in the nucleus exert a stronger electrostatic attraction on the outer electrons, increasing the ionisation energy.

2. Atomic Radius / Distance from Nucleus: Electrons in shells further from the nucleus experience a much weaker electrostatic pull (\(\text{force} \propto 1 / r^2\)), decreasing the ionisation energy.

3. Shielding (Screening): Inner electron shells repel the outer electrons and shield them from the full positive charge of the nucleus, decreasing the ionisation energy.

Evidence for Main Shells from Successive Ionisation Energies

If you plot the successive ionisation energies of an element against the number of electrons removed (usually plotted as \(\log_{10}(\text{Ionisation Energy})\) to fit the huge range on a graph), you will see clear patterns:

• Steady gradual increases occur when removing electrons from the same principal quantum shell, because the ion becomes progressively more positive.

• A sharp, massive jump occurs whenever an electron is removed from a new inner shell that is closer to the nucleus. An electron in an inner shell has significantly less shielding and is much closer to the nucleus, requiring a vastly larger amount of energy to detach.

Example: Determining the Group of an Unknown Element
Suppose element \(Y\) shows the following successive ionisation energies in \(\text{kJ mol}^{-1}\):
\(\text{IE}_1 = 738\)
\(\text{IE}_2 = 1451\)
\(\text{IE}_3 = 7733\)
\(\text{IE}_4 = 10543\)
Notice the enormous jump between \(\text{IE}_2\) and \(\text{IE}_3\) (from \(1451\) to \(7733\text{ kJ mol}^{-1}\)). This demonstrates that the first two electrons are relatively easy to remove because they reside in the outermost shell. The third electron must come from an inner shell closer to the nucleus. Therefore, element \(Y\) has 2 valence electrons and belongs to Group 2!

Quick Review & Key Takeaway: Successive ionisation energies always increase. Large, dramatic jumps reveal the boundary between principal quantum shells, allowing you to deduce the group number of an element.

4. Linking Spectra to Ionisation Energy Calculations

One of the most elegant connections in the Salters specification is linking the convergence limit of the Lyman series directly to the first ionisation energy of hydrogen.

At the convergence limit of the Lyman series, an electron absorbs exactly enough energy to jump from \(n = 1\) to \(n = \infty\). This transition corresponds to removing the electron from a single hydrogen atom:

\(\Delta E = h\nu_{\text{limit}}\)

To convert this energy per atom into the molar ionisation energy (\(\text{J mol}^{-1}\)), we multiply by the Avogadro constant, \(N_{\text{A}} = 6.02 \times 10^{23}\text{ mol}^{-1}\):

\(\text{First Ionisation Energy} = \Delta E \times N_{\text{A}} = h\nu_{\text{limit}} \times N_{\text{A}}\)

Step-by-Step Calculation Example

Question: The convergence limit of the Lyman series of hydrogen occurs at a frequency of \(\nu = 3.28 \times 10^{15}\text{ Hz}\). Calculate the first ionisation energy of hydrogen in \(\text{kJ mol}^{-1}\).

Step 1: Calculate the energy change per atom in Joules (\(\text{J}\))
Using the Planck constant from the Salters Data Sheet (\(h = 6.63 \times 10^{-34}\text{ J Hz}^{-1}\)):
\(\Delta E = h\nu = (6.63 \times 10^{-34}\text{ J Hz}^{-1}) \times (3.28 \times 10^{15}\text{ s}^{-1}) = 2.1746 \times 10^{-18}\text{ J}\)

Step 2: Multiply by the Avogadro constant to find the energy for 1 mole of atoms
Using \(N_{\text{A}} = 6.02 \times 10^{23}\text{ mol}^{-1}\):
\(\text{Energy per mole} = 2.1746 \times 10^{-18}\text{ J} \times 6.02 \times 10^{23}\text{ mol}^{-1} = 1.309 \times 10^6\text{ J mol}^{-1}\)

Step 3: Convert from Joules to kilojoules (\(\text{kJ mol}^{-1}\)) and round to appropriate significant figures
\(\text{First Ionisation Energy} = \frac{1.309 \times 10^6\text{ J mol}^{-1}}{1000} = 1310\text{ kJ mol}^{-1}\) (to 3 significant figures).

5. Summary and Common Exam Pitfalls

Here are the most frequent mistakes students make in examinations and how you can avoid them:

• Forgetting state symbols in ionisation equations: Writing \(\text{Na} \rightarrow \text{Na}^+ + \text{e}^-\) will score zero. You must always write \(\text{Na(g)} \rightarrow \text{Na}^+\text{(g)} + \text{e}^-\).

• Confusing the second ionisation equation: Students often mistakenly write \(\text{X(g)} \rightarrow \text{X}^{2+}\text{(g)} + 2\text{e}^-\). That equation represents the sum of the first and second ionisation energies! The second ionisation energy is strictly: \(\text{X}^+\text{(g)} \rightarrow \text{X}^{2+}\text{(g)} + \text{e}^-\).

• Mixing up units in spectral calculations: Always check whether the question asks for \(\text{J}\), \(\text{J mol}^{-1}\), or \(\text{kJ mol}^{-1}\). Remember to divide by \(1000\) when converting from \(\text{J mol}^{-1}\) to \(\text{kJ mol}^{-1}\).

• Confusing emission and absorption: In emission, electrons fall from higher levels to lower levels, releasing photons. In absorption, electrons jump from lower to higher levels, taking in photons.

• Balancing nuclear fusion equations: Always check both the top (mass numbers) and bottom (atomic numbers) to make sure they add up to the exact same total on both sides of the arrow.

Quick check

Can you answer these now?

Open each question to check the key ideas from this chapter.

What is nuclear fusion, and why does it require extremely high temperatures and pressures?

Nuclear fusion is the process where two light atomic nuclei collide and merge to form a heavier nucleus. Extremely high temperatures and pressures are required to provide sufficient kinetic energy and collision frequency to overcome the strong electrostatic repulsion between positively charged nuclei.

What two conservation laws must be satisfied when writing and balancing nuclear equations?

The sum of the mass numbers (nucleons, top numbers) and the sum of the atomic numbers (proton charges, bottom numbers) must be equal on both sides of the equation.

What is the difference between an atomic emission spectrum and an atomic absorption spectrum?

An emission spectrum consists of coloured lines on a dark background produced when excited electrons drop to lower energy levels and release photons, whereas an absorption spectrum consists of dark lines on a continuous background produced when ground-state electrons absorb specific frequencies of light to reach higher energy levels.

What experimental evidence indicates that electron energy levels in an atom are quantised?

The appearance of discrete line spectra rather than a continuous spectrum provides evidence that electrons can only occupy specific, fixed energy levels.

What causes spectral lines to converge in a series, and what does the convergence limit represent?

Lines converge because the energy levels get closer together as the principal quantum number \(n\) increases; the convergence limit represents the electron reaching \(n = \infty\), where it is completely removed from the nucleus (ionisation).

What is the definition of first ionisation energy?

The first ionisation energy is the energy required to remove one electron from each atom in one mole of gaseous atoms to form one mole of gaseous \(1+\) ions.

Why do successive ionisation energies always increase for any given element?

Successive electrons are being removed from an increasingly positive ion, which exerts a stronger electrostatic pull on the remaining electrons due to an increased proton-to-electron ratio.

What three main factors determine the magnitude of an ionisation energy?

Nuclear charge (number of protons), atomic radius (distance from nucleus), and shielding (screening by inner electron shells).

How do successive ionisation energies provide direct evidence for the existence of electron shells?

A large, sudden jump in successive ionisation energies indicates that an electron is being removed from a new inner shell that is closer to the nucleus with less shielding.

How is the first ionisation energy of hydrogen calculated from the convergence limit of the Lyman series?

By calculating the energy of a single photon at the convergence frequency using \(\Delta E = h\nu_{\text{limit}}\) and multiplying by the Avogadro constant \(N_{\text{A}}\) to obtain the molar energy.

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