Chapter 2: Atomic Structure

The Greek word atomos means “cannot be divided”. Democritus suggested that matter is made of tiny particles. Later, Dalton used atoms to explain how substances combine. Experiments then showed that atoms contain smaller particles.

The unit u is based on carbon-12: 1 u is one-twelfth of the mass of one carbon-12 atom. A proton is about 1836 times heavier than an electron.

A neutron is slightly heavier than a proton. Almost all the mass of an atom is in its nucleus.

A neutral atom has the same number of protons and electrons. Their charges balance. Ordinary hydrogen, ¹H, has one proton but no neutron.

J. J. Thomson identified the electron in 1897. He studied beams called cathode rays. Crookes had studied discharge tubes earlier. Faraday’s work also helped scientists understand electricity and matter.

A discharge tube is a glass tube with a small amount of gas inside. A vacuum pump removes most of the gas. Two metal terminals connect to a high-voltage supply. The negative terminal is the cathode. The positive terminal is the anode.

High voltage produces a beam of electrons. It travels from the cathode towards the anode. The beam can make the glass or a screen glow. This glow is fluorescence: the material takes in energy and gives out light.

An opaque object blocks the beam. Kinetic energy means energy of motion. The charge-to-mass ratio tells us how much charge a particle has for its mass.

Magnitude of electron charge-to-mass ratio: |e|/m_e ≈ 1.759 × 10¹¹ C kg⁻¹ = 1.759 × 10⁸ C g⁻¹. The electron’s charge is negative; C denotes coulomb, the charge unit.

In 1886, Goldstein used a cathode with holes in it. Positive gas ions moved towards the negative cathode. Some passed through the holes. These streams were called canal rays.

Canal rays come from gas particles that lose electrons. They do not come out of the anode. One fast electron can knock an electron out of a gas particle:

M + e⁻ → M⁺ + 2e⁻.

One electron enters. Two electrons leave, along with a positive ion.

Without a deflecting field, the rays travel roughly straight.

Positive ions bend towards a negative electric plate.

Their charge-to-mass ratio depends on the gas and the ion.

The ions are much heavier than electrons.

The lightest positive ion is H⁺. It is the nucleus of hydrogen: one proton. Canal rays made from other gases contain other positive ions. Rutherford later identified hydrogen nuclei produced in nuclear reactions. He reported this work in 1919.

Example: ¹⁴₇N + ⁴₂He → ¹⁷₈O + ¹₁H.

Mass numbers: 14 + 4 = 17 + 1.

Atomic numbers: 7 + 2 = 8 + 1.

The emitted ¹₁H nucleus is a proton.

In 1932, James Chadwick directed alpha particles at beryllium. Beryllium gave out radiation that knocked protons out of paraffin wax. The results showed that the radiation contained particles with no charge. Their mass was close to that of a proton. Chadwick had found neutrons.

An alpha particle is a helium nucleus: 2 protons and 2 neutrons. Bombardment means sending fast particles towards a target.

⁹₄Be + ⁴₂He → ¹²₆C + ¹₀n.

Mass numbers: 9 + 4 = 12 + 1.

Atomic numbers: 4 + 2 = 6 + 0.

A neutron has no charge. Its mass is about 1 u. Neutrons are found in most atomic nuclei. An electric field does not directly bend their paths. Their ability to pass through matter depends on their energy and the material.

Geiger and Marsden carried out the experiment under Rutherford’s direction. Rutherford used their results to suggest the nuclear model in 1911.

Positive alpha particles passed through a narrow opening in a lead block. This made a narrow beam. The beam hit thin gold foil. A zinc sulfide screen gave a tiny flash wherever a particle arrived. A change in a particle’s direction is called scattering.

The nucleus is small and positively charged.

It contains almost all the mass of the atom.

Electrons are outside the nucleus. Rutherford pictured them moving around it.

In a neutral atom, positive and negative charges balance.

The nucleus is much smaller than the whole atom.

The experiment showed that positive charge is concentrated in a small nucleus. Neutrons were discovered later. They were not part of Rutherford’s original 1911 model.

1. The model could not explain why an atom stays stable. Classical physics says that an electron in a circular path should lose energy. It would then spiral into the nucleus.

2. The model could not explain why atoms give out only certain colours of light.

A spectrum shows radiation arranged by wavelength or frequency. A line spectrum has separate lines with gaps between them. A continuous spectrum has a full range without gaps. Atoms give line spectra.

In 1913, Niels Bohr suggested that electrons can have only certain energies. This helped explain hydrogen’s line spectrum. Quantized means “only certain values are allowed”.

1. In the Bohr model, electrons occupy allowed circular orbits of definite energy.

2. An electron in an allowed stationary state does not radiate energy. Stationary means its energy stays constant, not that it stops moving.

3. An electron moves to a higher level when it absorbs energy. A drop to a lower level emits a photon—a packet of electromagnetic radiation.

4. The energy change equals the photon energy: |ΔE| = hν.

5. Allowed angular momentum: mvr = nh/(2π), where n = 1, 2, 3, … .

The number n labels the main energy level. Levels 1, 2, 3 and 4 are called K, L, M and N. The lowest allowed state is the ground state. An atom with extra energy is in an excited state.

h is the Planck constant: about 6.626 × 10⁻³⁴ J s. The symbol ν is frequency: the number of cycles each second. In mvr, m is electron mass, v is speed and r is orbit radius. Angular momentum describes motion around a centre.

Only certain energy levels are allowed. An electron can therefore give out only certain photon energies.

E(high) − E(low) = hν.

A bigger energy gap gives a photon with a higher frequency.

Bohr’s model works well for species with one electron: H, He⁺, Li²⁺ and Be³⁺. It does not fully explain atoms with several electrons. It also misses some fine details of spectra and the effects of electric and magnetic fields.

A magnetic field can split spectral lines: the Zeeman effect. An electric field can also split them: the Stark effect. The uncertainty principle says we cannot know an electron’s exact position and exact momentum together. A fixed classical path does not fit this idea.

H⁺ has no electron, so it is not a one-electron species. Bohr’s circular orbits belong to a historical model. Modern theory does not give electrons fixed circular paths.

In 1900, Planck suggested that energy is taken in or given out in small packets. In 1905, Einstein used packets of light, called photons, to explain the photoelectric effect. In this effect, suitable light knocks electrons out of a material.

Photon energy: E = hν.

Wave relation for light in vacuum: c = νλ.

Hence E = hc/λ.

λ (lambda) = wavelength; c = speed of light. A shorter wavelength means higher photon energy.

Matter can show both particle and wave behaviour. The de Broglie wavelength is λ = h/p, where p is momentum. At speeds much lower than light speed, p = mv. So λ = h/(mv).

For a photon, E = pc and E = hc/λ.

Therefore pc = hc/λ.

Cancel c: p = h/λ, giving λ = h/p.

de Broglie extended this wavelength–momentum relationship to matter. He proposed that matter also follows this relation. An electron is not a photon.

E = mc² gives rest energy: energy linked to mass even when an object is at rest. It does not give an electron’s energy of motion. For the electron’s wavelength, use λ = h/p. At low speeds, p ≈ mv.

Electron diffraction is evidence of wave behaviour. Waves spread and form patterns when they meet obstacles or openings.

Greater momentum means a shorter wavelength.

Everyday objects have wavelengths too small to notice in daily life.

In 1926, Schrödinger developed a wave equation for electrons. It helps predict where an electron is likely to be. It does not give a fixed circular path. Probability means the chance of finding something.

An atomic orbital describes an allowed electron state and where the electron is likely to be found. It is described mathematically by a wavefunction. In an electron-cloud picture, a denser region means a greater chance of finding the electron there.

Subshells are labelled s, p, d and f. Each contains one or more orbitals. An s orbital is spherical. A p orbital has two main lobes. The d and f shapes are more complex.

A shell contains electron states with the same principal quantum number, n. This number labels the main energy level. K, L, M, N, O and P correspond to n = 1–6. A shell is an energy-level group, not a physical ring.

A subshell is a division of a shell containing orbitals of the same type. Each orbital holds at most two electrons.

In hydrogen, a higher n means higher energy. In atoms with several electrons, subshell type also matters. For example, 4s starts filling before 3d. An inner shell does not always fill to its full capacity before the next shell starts.

1. Find the number of electrons. For a neutral atom, it equals Z.

2. Fill lower-energy orbitals first.

3. Keep within each orbital’s and subshell’s capacity.

4. Add the superscripts. Their total must equal the number of electrons.

For the first 18 elements: 1s → 2s → 2p → 3s → 3p. In 2p⁴, 2 labels the shell, p the subshell and 4 the electrons in it.

The M shell can hold up to 18 electrons. In the first 18 elements, only its 3s and 3p subshells fill. Argon is therefore 2,8,8. This does not mean that the M shell can hold only 8 electrons.

Some isotopes have unstable nuclei. Their nuclei change on their own and give out radiation. We can use a detectable isotope as a tracer to follow a substance. Radiation is also used for treatment, sterilizing equipment and producing power.

Radiotherapy uses radiation to treat disease. Sterilization destroys living microorganisms. Fission splits a heavy nucleus. Technetium-99m has extra nuclear energy and changes after a short time. The m stands for metastable.

Choose an isotope to suit the task. Its radiation and lifetime both matter. Radioactive decay changes the nucleus. An ordinary chemical reaction does not.

The thyroid is a gland in the neck. It helps control metabolism: the body’s chemical reactions.

³⁵₁₇Cl: 17 p, 18 n, 17 e; shells 2, 8, 7.

³⁷₁₇Cl: 17 p, 20 n, 17 e; shells 2, 8, 7.

Same Z = 17, different A = 35 and 37: they are isotopes.

For the first-18-element ground-state arrangement:

(a) K = 2, L = 8, M = 5. Total = 15 electrons; a neutral atom has Z = 15.

(b) Shells: 2, 8, 5; subshells: 1s² 2s² 2p⁶ 3s² 3p³.

(c) Element: phosphorus, P.

This answer assumes a neutral atom in its lowest-energy, or ground, state. The M-shell count alone is not enough if the particle is an ion or is in an excited state.

Classical orbiting electrons should radiate energy and spiral into the nucleus, so the model cannot explain stability. It also does not explain discrete line spectra.

Electrons and other matter exhibit particle and wave behaviour. Their wavelength is λ = h/p, or approximately h/(mv) at low speeds. Electron diffraction provides evidence of wave behaviour.

It works mainly for one-electron species. It does not adequately explain multi-electron spectra, fine details or field-induced splitting. A fixed electron path conflicts with the uncertainty principle.

Both have Z = 8: 8 protons and, if neutral, 8 electrons, with configuration 1s² 2s² 2p⁴. Oxygen-17 has 17 − 8 = 9 neutrons; oxygen-16 has 16 − 8 = 8. They are isotopes with very similar chemical behaviour but different masses.

A narrow alpha beam struck thin gold foil. A zinc sulfide screen detected particles as flashes. Most passed almost straight through; a few deflected; very few returned.

Hence the atom has a tiny dense positive nucleus and a much larger surrounding region occupied by electrons. Nearly all mass is nuclear. The experiment did not establish neutrons or fixed energy shells.

Cobalt-60: selected radiotherapy and medical-material sterilization.

Iodine-123: thyroid imaging; iodine-131: selected thyroid treatments.

Technetium-99m: diagnostic imaging, including bone scans.

Americium-241: ionization smoke detectors.

Uranium-235: nuclear-reactor fuel.

Carbon-14: dating once-living material.

Gold-198 and technetium-labelled tracers: specialist flow and environmental studies.

Phosphorus-32 and strontium-90: selected specialist beta-radiation treatments.

Plutonium-238: heat-based power, historically including some pacemaker batteries.

Planck–Einstein photon relation: E = hν.

Since c = νλ, E = hc/λ.

For a photon, E = pc.

Equate: pc = hc/λ.

Cancel c: p = h/λ, so λ = h/p.

de Broglie proposed this relation for matter too. For a slow electron, p ≈ mv, giving λ ≈ h/(mv). Do not substitute the rest-energy expression mc² for the kinetic energy of a slow electron.

A discharge tube contains low-pressure gas, electrodes and a high-voltage supply. Cathode rays are streams of electrons moving from the negative cathode towards the anode.

They travel straight without deflecting fields, cast shadows, cause fluorescence, carry energy and momentum, and bend towards a positive electric plate. Magnetic fields also deflect them.

Their charge-to-mass ratio stays the same when the gas or electrode material is changed. This shows that atoms of all elements contain electrons.

Schrödinger’s wave equation describes allowed electron states. A wavefunction is the mathematical description used to find where an electron is likely to be. An orbital is an electron state, not a fixed path.

A denser electron cloud means a greater chance of finding the electron there. Orbitals form subshells, and subshells form shells. s orbitals are spherical; p orbitals have two lobes.

The model includes the wave nature of electrons.

Electron: Thomson’s cathode rays had negative charge and a common charge-to-mass ratio.

Proton: positive hydrogen ions are hydrogen nuclei; Rutherford identified hydrogen nuclei ejected in nuclear reactions. Goldstein’s canal rays established positive gas ions, not protons in every gas.

Neutron: Chadwick’s beryllium radiation ejected protons from wax, demonstrating neutral particles with masses close to a proton.

For each neutral atom: protons = Z; electrons = Z; neutrons = A − Z.

(a) Oxygen with 8 protons has Z = 8.

(b) Chlorine with 17 protons and 18 neutrons has A = 17 + 18 = 35.

(c) ⁵⁹₂₇Co: 27 protons, 59 − 27 = 32 neutrons, 27 electrons if neutral.

(d) Ordinary hydrogen, ¹H, has no neutron.

Protons and neutrons account for nearly all atomic mass. Rutherford used classical electron motion, which predicts continuous energy loss; Bohr introduced quantized stationary states and discrete transitions. Living processes such as digestion and respiration involve chemical reactions.

(a) s subshell: maximum 2 electrons.

(b) Neutral Z = 11: shells 2, 8, 1; L contains 8 electrons.

(c) K fills first in ground-state atoms because 1s has the lowest energy.

(d) Full K + full L = 2 + 8 = 10 electrons.

Tritium has the most neutrons among hydrogen isotopes: 2. Isotopes have very similar chemical behaviour because neutral atoms share the same electron configuration; masses differ because neutron counts differ.

Carbon isotopes all have 6 protons; hydrogen isotopes all have 1 proton. Their neutron numbers vary within each element.