Structure of Atom: Discovering Particles and Bohr's Model

In the mid-1850s, scientists began studying what happened when electricity was passed through a partially evacuated glass tube fitted with two metal electrodes, a cathode ray discharge tube. At very low pressure and very high voltage, a stream of particles flowed from the negative electrode toward the positive one, glowing where they struck a phosphorescent coating. These cathode rays travelled in straight lines, bent toward a positively charged plate when an electric field was applied, and behaved identically regardless of which metal the electrodes were made of or which gas filled the tube. In 1897, J.J. Thomson measured the ratio of charge to mass, e/me, for these particles, by carefully balancing electric and magnetic fields against each other, and got the same answer every single time, no matter the source. Whatever these particles were, they were a fundamental, universal constituent of every kind of atom, and Thomson called them electrons.

Knowing the charge-to-mass ratio wasn't enough; chemists needed the electron's actual charge to work out its actual mass. R.A. Millikan solved this between 1906 and 1914 with his oil drop experiment: fine oil droplets were sprayed into a chamber, ionised by X-rays so they picked up a static charge, and their fall was slowed, stopped, or reversed entirely by adjusting an electric field across the chamber. By measuring exactly how strong a field was needed to hold a given droplet motionless against gravity, Millikan found that the charge on every droplet was always a whole-number multiple of one fixed value, roughly -1.6 x 10^-19 coulombs. That fixed value had to be the charge of a single electron, since nothing smaller ever turned up. Combining this charge with Thomson's earlier e/me ratio then gave the electron's mass directly: about 9.109 x 10^-31 kg, nearly 1836 times lighter than a hydrogen atom.

A modified cathode ray tube revealed a second stream of particles moving the opposite way, from anode to cathode, called canal rays. Unlike electrons, these were positively charged, and their mass depended entirely on which gas filled the tube, since they were simply the positively charged remnants of that gas's own atoms, stripped of electrons. The smallest and lightest of these, obtained from hydrogen gas, was characterised in 1919 and named the proton. A third particle remained elusive for over a decade, since it would need to carry no charge at all, making it invisible to every electric or magnetic detection method used so far. James Chadwick finally found it in 1932, by bombarding a thin sheet of beryllium with alpha particles and detecting electrically neutral particles, slightly heavier than protons, being knocked loose. He named them neutrons, completing the trio of subatomic particles.

With electrons known, Thomson proposed in 1898 that an atom was a uniform sphere of positive charge, roughly 10^-10 m across, with electrons embedded in it like plums in a pudding, or seeds in a watermelon, arranged to give the most stable overall configuration. It correctly explained the atom's overall neutrality, but it made a clear, testable prediction: since the positive charge was spread evenly through the whole atom, anything fired at it should pass through with at most a small deflection. Rutherford, along with Hans Geiger and Ernest Marsden, tested exactly this by directing a stream of high-energy alpha particles at an extremely thin sheet of gold foil, surrounded by a fluorescent screen that flashed wherever a particle struck it. If Thomson's model were correct, every alpha particle should have sailed through with barely a wobble.

The gold foil experiment's results were nothing like Thomson's model predicted. Most alpha particles passed straight through undeflected, exactly as expected, but a small fraction deflected at small angles, and, most startling of all, about 1 in 20,000 bounced almost straight back, deflected by nearly 180 degrees. Rutherford concluded that an atom is mostly empty space, since nearly every particle passed through undisturbed; that a tiny, dense, positively charged core, the nucleus, must account for the rare sharp deflections, since only a concentrated charge could repel an alpha particle that strongly; and that this nucleus occupies a volume vastly smaller than the atom itself, roughly the ratio of a cricket ball to a five-kilometre radius. Rutherford's resulting model placed a dense nucleus at the centre, with electrons orbiting it much like planets around the sun, held in place by electrostatic attraction rather than gravity.

Once protons and neutrons were both known to reside in the nucleus, two numbers became essential. The atomic number (Z) is simply the number of protons in the nucleus, which equals the number of electrons in a neutral atom, since positive and negative charge must balance. The mass number (A) is the total count of protons and neutrons together, the nucleons. Atoms of the same element always share the same atomic number, but can differ in neutron count, and therefore in mass number, giving rise to isotopes: hydrogen exists as protium (1 proton, 0 neutrons), deuterium (1 proton, 1 neutron), and tritium (1 proton, 2 neutrons), all chemically identical since chemical behaviour depends on electron count, not neutron count. Isobars, by contrast, are atoms of different elements that happen to share the same mass number despite having different atomic numbers, such as carbon-14 and nitrogen-14.

Rutherford's solar-system model had a fatal theoretical flaw. Maxwell's electromagnetic theory establishes that any charged particle undergoing acceleration must emit electromagnetic radiation, and an electron circling a nucleus is constantly accelerating, since its direction is always changing even at constant speed. Emitting radiation costs energy, so a circling electron should continuously lose energy and spiral inward, with calculations showing it should crash into the nucleus in about 10^-8 seconds. Every atom should therefore be unstable and short-lived, yet ordinary matter is neither. Making the electrons stationary instead doesn't solve the problem either, since electrostatic attraction would simply pull them straight into the nucleus, collapsing the atom into a miniature version of Thomson's already-discredited model. Rutherford's model, in other words, correctly located the nucleus and the electrons but had nothing to say about why the atom holds together at all, a gap that would take an entirely new theory to fill.

Resolving the stability puzzle required first understanding electromagnetic radiation itself, since Bohr's eventual solution would borrow ideas from exactly this field. Maxwell showed that an accelerating charged particle produces oscillating electric and magnetic fields that propagate outward as waves, needing no medium to travel through, all moving at the same speed in vacuum, roughly 3.0 x 10^8 m/s, the speed of light, symbol c. These waves are characterised by frequency (v, the number of waves passing a point per second, in hertz) and wavelength (lambda, the physical distance between successive crests), related by c = vλ. The full electromagnetic spectrum spans an enormous range, from radio waves around 10^6 Hz through microwave, infrared, the razor-thin visible band around 10^15 Hz that human eyes can actually detect, ultraviolet, and on to X-rays and gamma rays, each region differing only in frequency and wavelength, not in fundamental nature.

Classical wave theory could explain diffraction and interference perfectly well, but it failed completely at explaining black body radiation, the light emitted by a heated object as a function of wavelength and temperature. Max Planck resolved this in 1900 with a radical assumption: atoms and molecules can emit or absorb energy only in discrete chunks, never continuously, with each chunk's energy proportional to its frequency, E = hv, where h is Planck's constant, 6.626 x 10^-34 J s. He called the smallest such packet a quantum. Planck compared this to standing on a staircase: a person can stand on any individual step, but never in between two steps. This single assumption, energy restricted to E = 0, hv, 2hv, 3hv... and nothing in between, let Planck perfectly reproduce the observed black body radiation curves, something continuous wave theory had never managed.

In 1887, Hertz observed that shining light on certain metals ejected electrons instantly, with no time lag, but only above a specific threshold frequency unique to that metal, no matter how bright the light was below it; above that threshold, the ejected electrons' kinetic energy increased with frequency, not brightness, while brightness only affected how many electrons came out. None of this fit classical wave theory, which predicted energy should simply accumulate from any frequency of light given enough time. Einstein resolved it in 1905 by extending Planck's quantum idea: light itself consists of discrete packets, photons, each carrying energy hv. A photon transfers its entire energy to one electron instantly on collision; if that energy exceeds the metal's own work function (the minimum energy needed to free an electron), the excess becomes the ejected electron's kinetic energy, exactly matching every one of Hertz's observations.

Niels Bohr combined Planck's quantum idea with Rutherford's nuclear model in 1913 to finally explain hydrogen's stability and spectrum. He postulated that an electron moves only in specific circular orbits of fixed radius and energy, called stationary states, arranged concentrically around the nucleus; that an electron's energy in a given orbit does not change over time, so radiation is neither absorbed nor emitted while it stays there, directly sidestepping the collapse problem; that an electron can jump between stationary states by absorbing or emitting exactly the energy difference between them, with the resulting radiation's frequency given by Bohr's frequency rule, v = (E2 - E1)/h; and that an electron's angular momentum is itself quantised, restricted to whole-number multiples of h/2π. This last postulate is what actually restricts an electron to only certain orbits in the first place, and explains why Maxwell's continuous-radiation prediction simply doesn't apply here.

Hydrogen gas, excited by an electric discharge, emits light only at specific discrete wavelengths, not a continuous rainbow, producing a line spectrum unique to each element, like a fingerprint. Bohr's model explained this precisely: since orbit energies are quantised at En = -RH(1/n^2), with RH the Rydberg constant, an electron falling from a higher orbit ni to a lower orbit nf releases energy equal to the difference between them, appearing as light of one exact frequency. Every possible transition between orbits produces its own spectral line, and transitions ending at n=1 (the Lyman series) fall in the ultraviolet, those ending at n=2 (the Balmer series) fall in the visible range, the only series the human eye can see directly, and those ending at n=3, 4, or 5 (Paschen, Brackett, Pfund) fall in the infrared. This was a genuine triumph: a formula chemists had found by pattern-matching experimental data years earlier, Rydberg's, fell directly out of Bohr's theoretical model.

Bohr's model was a genuine leap forward, correctly explaining hydrogen's stability and its entire spectrum, but it had real limits. It failed to explain the finer structure seen with sophisticated spectroscopy, closely spaced doublet lines, and could not account for the spectrum of any atom with more than one electron, not even helium. It offered no explanation for the splitting of spectral lines under a magnetic field (the Zeeman effect) or an electric field (the Stark effect), and said nothing whatsoever about how atoms combine to form molecules through chemical bonds. The underlying reason for all these failures was the same: Bohr treated the electron as a simple charged particle tracing a precisely defined circular path, ignoring its wave nature entirely, and a precisely defined path can only exist if both an electron's exact position and exact velocity are known simultaneously, something the still-undiscovered Heisenberg uncertainty principle would soon rule out completely. A genuinely new mechanics, built from the ground up around the electron's dual nature, was needed.