Structure of Atom
1. What This Chapter Covers
From the previous class you know the three sub-atomic particles — negatively charged electrons, positively charged protons and electrically neutral neutrons — and the atomic models of J.J. Thomson, Ernest Rutherford and Niels Bohr.
Activity 1 asks you to build a model of an atom from that knowledge and present it in class, then compare it with your friends' models and ask:
- Do all atoms have the same sub-atomic particles?
- Why is an atom of one element different from the atoms of another?
- How are the electrons distributed in an atom?
The chapter's answer is that you cannot settle these by reasoning about particles alone. You have to look at light — at coloured flames and at spectra. It is allotted 7 periods across August and September, and runs from textbook page 224 to page 256.
What makes the chapter worth following in order is that each model is discarded for a specific observational reason, not simply replaced.
2. The Wave Nature of Light (Textbook 6.1)
A rainbow has seven colours — VIBGYOR — spreading continuously, with the intensity of each varying from point to point.
Throwing a stone into a still pond produces ripples that carry the disturbance outwards as waves. Sound waves are produced when something vibrates, like a drum. In the same way, electromagnetic waves are produced when an electric charge vibrates.
A vibrating electric charge creates a change in the electric field, that change creates a change in the magnetic field, and the process continues — with both fields perpendicular to each other and both at right angles to the direction of propagation.
Visible light is an electromagnetic wave, and the speed of light is c = 3 × 10⁸ m s⁻¹.
Characteristics of an electromagnetic wave (6.1.1)
| Quantity | Definition |
|---|---|
| Wavelength (λ) | The distance from one crest or trough to the next |
| Frequency (ν) | The number of waves passing a given point per unit time, in reciprocal seconds |
They are related by
c = νλ
This is a universal relationship applying to all waves. Since c is fixed, λ is inversely proportional to ν: as frequency increases, wavelength becomes smaller.
The electromagnetic spectrum (6.1.2)
The entire range of electromagnetic wavelengths is the electromagnetic spectrum. It is continuous, running from gamma rays at the short-wavelength end to radio waves at the long-wavelength end, taking in cosmic rays, X-rays, ultraviolet, visible light, infrared, microwaves and radar along the way.
Our eyes are sensitive to only a narrow band of it. Each colour in a rainbow corresponds to a specific wavelength, from red at the longer wavelength to violet at the shorter, and that range is the visible spectrum.
3. Planck and Discrete Energy
Heating an iron rod
Heat an iron rod in a flame and some of the heat energy is emitted as light. It first turns red — lower energy, longer wavelength — and as the temperature rises it glows orange, yellow, then blue, which is higher energy and shorter wavelength, and finally white if the temperature is high enough, since white contains all visible wavelengths.
Other colours are emitted at the same time, but one colour dominates in intensity so the others cannot be observed.
Planck's break with tradition
Max Planck broke with the continuous-energy tradition by assuming energy is always absorbed or emitted in multiples of hν — that is, hν, 2hν, 3hν, up to nhν.
E = hν
where h is Planck's constant, 6.626 × 10⁻³⁴ J s, and ν is the frequency absorbed or emitted.
So the energy of red light, with its longer wavelength and lower frequency, is lower than that of blue light. And the energy emitted by a body increases with temperature.
The significance of Planck's proposal is that electromagnetic energy can be gained or lost in discrete values, not continuously.
Hence an emission or absorption spectrum is a collection of a group of wavelengths, not a smooth continuum.
Activity 2 — flame tests
Take a pinch of cupric chloride in a watch glass and make a paste with concentrated hydrochloric acid. Put the paste on a platinum loop and introduce it into a non-luminous flame. Repeat with strontium chloride.
- Cupric chloride gives a green flame.
- Strontium chloride gives a crimson red flame.
- Sodium vapour gives the yellow light of street lamps.
Each element emits its own characteristic colour. These correspond to certain discrete wavelengths and are called line spectra.
The lines in atomic spectra can be used to identify unknown atoms, just as fingerprints identify people.
4. Bohr's Model and Its Limitation (Textbook 6.2)
Niels Bohr proposed an atomic model based on the hydrogen atomic spectrum. His postulates:
- Electrons occupy stationary orbits of fixed energy at different distances from the nucleus.
- An electron absorbs energy when it jumps from a lower to a higher energy state, and emits energy when it falls back.
- The energies can have only certain values E₁, E₂, E₃ — the energy is quantised. These states are stationary states and the permitted energies are energy levels.
The lowest energy state is the ground state. Absorbing energy takes the electron to an excited state, but it does not stay there long. On returning, it emits the energy as electromagnetic radiation of a specific wavelength — and if that wavelength is in the visible region, it appears as an emission line.
Bohr's model explains all the line spectra of the hydrogen atom, and is a successful model as far as hydrogen is concerned.
But viewed through a high-resolution spectroscope, the hydrogen lines appear as groups of finer lines. Bohr's model failed to account for that splitting.
5. The Bohr-Sommerfeld Model (Textbook 6.3)
To account for the fine structure, Sommerfeld modified Bohr's model by adding elliptical orbits.
He kept Bohr's first circular orbit as it was, added one elliptical orbit to the second orbit, two to the third, and so on, with the nucleus at one of the principal foci of each ellipse. His reasoning was general: periodic motion under a central force leads to elliptical orbits with the centre of force at a focus.
This model succeeded for the fine structure of hydrogen, but it failed for atoms with more than one electron, and does not give a satisfactory picture of atomic structure in general.
The chapter's structure is a sequence of failures, each specific. Knowing what defeated each model is usually what the exam question is really asking.
6. The Quantum Mechanical Model (Textbook 6.4)
Why a definite path is impossible
If the electron revolved in a defined orbit, its exact position at any time would be known. To check that, we would need to know both its position and its velocity.
Electrons are invisible. To find an object in the dark we shine a torch on it, and the same must be done here — but because electrons are very small, light of very short wavelength is required.
That short-wavelength light interacts with the electron and disturbs its motion. So position and velocity cannot be measured accurately at the same time.
It follows that electrons do not follow definite paths in an atom, and therefore an atom does not have a definite boundary. An electron cannot be pinpointed.
Orbitals
To handle this, Erwin Schrodinger developed the quantum mechanical model. Instead of Bohr's orbits, electrons are thought to exist in a particular region of space around the nucleus at a given instant.
The region of space around the nucleus where the probability of finding the electron is maximum is called an orbital.
Only certain orbitals can exist in the space around a nucleus, and each stable-energy orbital is described by a particular set of quantum numbers.
7. The Four Quantum Numbers (Textbook 6.5)
Principal quantum number, n (6.5.1)
Related to the size and energy of the main shell. It takes positive integer values 1, 2, 3 and so on.
As n increases, the shells become larger, the electrons are farther from the nucleus, and the energy is higher. For each n value there is one main shell:
| Shell | K | L | M | N |
|---|---|---|---|---|
| n | 1 | 2 | 3 | 4 |
Angular momentum quantum number, l (6.5.2)
For each value of n, l takes integer values from 0 to n − 1, and each l value represents one sub-shell. Each l is related to the shape of that sub-shell:
| l | 0 | 1 | 2 | 3 |
|---|---|---|---|---|
| Sub-shell | s | p | d | f |
So when n = 1 there is only one sub-shell, l = 0, designated 1s. When n = 2 there are two, the 2s sub-shell with l = 0 and the 2p sub-shell with l = 1.
Magnetic quantum number, m_l (6.5.3)
Takes integer values between −l and +l including zero, so there are (2l + 1) values for a given l:
−l, (−l + 1), ..., −1, 0, 1, ..., (+l − 1), +l
These describe the spatial orientation of the orbital relative to the others.
When l = 0, there is one value and so one orbital, the s orbital. When l = 1 there are three values −1, 0, +1, giving three p orbitals oriented along the x, y and z axes, labelled p_x, p_y and p_z.
Orbitals in a sub-shell belonging to the same shell have the same energy, and are called degenerate orbitals.
| Sub-shell | Number of orbitals (2l + 1) | Maximum electrons |
|---|---|---|
| s (l = 0) | 1 | 2 |
| p (l = 1) | 3 | 6 |
| d (l = 2) | 5 | 10 |
| f (l = 3) | 7 | 14 |
Each sub-shell holds a maximum of twice as many electrons as it has orbitals.
The shapes: s orbitals are spherical, p orbitals are dumbbell-shaped, and d orbitals are double dumbbell-shaped.
Spin quantum number, m_s (6.5.4)
The first three numbers describe the size, shape and orientation of an orbital. A fourth is needed because of an observation: the yellow light of a sodium vapour street lamp, examined under a high-resolution spectroscope, is a very closely spaced doublet. Alkali and alkaline earth metals show such lines.
The spin quantum number refers to the two possible orientations of the spin of an electron, one clockwise and one anticlockwise, represented by +1/2 and −1/2. If both electrons have the same sign the spins are parallel; otherwise they are anti-parallel.
Its importance shows when electrons occupy specific orbitals in multi-electron atoms.
8. Electronic Configuration (Textbook 6.6)
The distribution of electrons in shells, sub-shells and orbitals is the electronic configuration, written in shorthand as
n l ˣ
where n is the principal energy level, l is the letter for the sub-level, and x is the number of electrons in that sub-shell, written as a superscript.
For hydrogen, Z = 1, so the configuration is 1s¹, with quantum numbers n = 1, l = 0, m_l = 0 and m_s = +1/2 or −1/2.
For atoms with more than one electron, three principles are needed.
The Pauli Exclusion Principle (6.6.1)
No two electrons of the same atom can have all four quantum numbers the same.
If n, l and m_l are the same for two electrons, then m_s must differ. So in helium the two electrons in 1s must have paired, anti-parallel spins, one with +1/2 and the other with −1/2, giving 1s².
The major consequence concerns orbital occupancy: since only two values of m_s are allowed, an orbital can hold only two electrons, and they must have opposite spins.
The Aufbau Principle (6.6.2)
As we pass to each element of next higher atomic number, one electron is added.
- The maximum number of electrons in any shell is 2n².
- The maximum in a sub-shell is 2(2l + 1), giving 2, 6, 10 and 14 for s, p, d and f.
In the ground state, the configuration is built by placing electrons in the lowest available orbitals until the total equals the atomic number.
"Aufbau" is German for "building up". Two rules predict the order:
- Electrons are assigned in order of increasing (n + l).
- For sub-shells with the same (n + l), electrons go first to the one with lower n.
This gives the ascending order of energies, shown by the Moeller chart:
1s < 2s < 2p < 3s < 3p < 4s < 3d < 4p < 5s < 4d < 5p < 6s < 4f < 5d < 6p < 7s < 5f < 6d < 7p < 8s
The first few elements follow directly:
| Element | Z | Configuration |
|---|---|---|
| H | 1 | 1s¹ |
| He | 2 | 1s² |
| Li | 3 | 1s² 2s¹ |
| Be | 4 | 1s² 2s² |
| B | 5 | 1s² 2s² 2p¹ |
Hund's Rule (6.6.3)
For carbon, Z = 6, the question is where the sixth electron goes — does it pair up in the same p orbital, or go to the next one?
Electron pairing in orbitals starts only when all available degenerate orbitals are singly occupied.
So carbon is 1s² 2s² 2p²: the first four electrons fill 1s and 2s, and the next two go into separate 2p orbitals with parallel spins.
Activity 3 asks you to complete the configurations for C, N, O, F, Ne, Na, Mg, Al, Si, P, S, Cl, Ar, K and Ca — which is the best practice available for all three rules together.
Key words from the chapter
Wave, spectrum, discrete energy, line spectrum, orbital, quantum numbers, shell, sub-shell, shapes of orbitals, electron spin, electronic configuration, the Pauli exclusion principle, Aufbau principle, Hund's rule.
9. Summary
Light is characterised by wavelength and frequency, related by c = νλ, and the full range of wavelengths is the electromagnetic spectrum, of which the visible band is a small part. A spectrum is a group of wavelengths.
Heating an iron rod, and the flame colours of cupric chloride, strontium chloride and sodium, show that elements emit characteristic discrete wavelengths — line spectra, which identify atoms the way fingerprints identify people. Planck explained this by proposing that electromagnetic energy is gained or lost only in discrete amounts, E = hν, with h = 6.626 × 10⁻³⁴ J s.
Bohr's model placed electrons in stationary states of quantised energy, with absorption raising an electron to an excited state and emission returning it to the ground state. It explained the hydrogen line spectrum but not the splitting into finer lines. Sommerfeld added elliptical orbits and explained the fine structure, but failed for multi-electron atoms.
The deeper problem is that position and velocity cannot both be measured accurately, since the short-wavelength light needed to locate an electron disturbs its motion. So electrons have no definite paths and atoms no definite boundary. Schrodinger's quantum mechanical model replaces orbits with orbitals — regions where the probability of finding the electron is maximum.
Each orbital is described by quantum numbers: n for size and energy, l for shape with values 0 to n − 1, m_l for orientation with (2l + 1) values, and m_s for spin with values +1/2 and −1/2. Sub-shells s, p, d and f hold 2, 6, 10 and 14 electrons.
Configurations are written as n l ˣ and built using three rules: Pauli, that no two electrons share all four quantum numbers, so an orbital holds two electrons of opposite spin; Aufbau, that the lowest-energy orbitals fill first in order of increasing (n + l), and for equal (n + l) the lower n first; and Hund's rule, that degenerate orbitals are singly occupied with parallel spins before any pairing begins.
