Structure of the atom

Before 1911, the accepted model of the atom was J.J. Thomson's 'plum pudding' model, which proposed that an atom was a sphere of positive charge with negative electrons embedded within it. This was overturned by the Geiger-Marsden experiment, famously interpreted by Ernest Rutherford. In this experiment, a narrow beam of positively charged alpha particles was fired at a very thin sheet of gold foil inside a vacuum. A detector was moved around the foil to count the number of alpha particles scattered at different angles. The results were startling:

1. Most alpha particles passed straight through the foil with no deflection. This implied that the atom is mostly empty space.
2. A small number of particles were deflected by small angles. This suggested the presence of a concentration of positive charge that repelled the alpha particles.
3. A very tiny fraction (about 1 in 8000) were deflected by large angles, some even 'bouncing back' (scattered by more than 90°). This could only happen if the atom's positive charge and mass were concentrated in a very small, dense region, which Rutherford called the nucleus.

These observations led to the Rutherford nuclear model: a dense, massive, positively charged nucleus at the centre, with tiny, negatively charged electrons orbiting it at a relatively large distance. The electrostatic force of attraction between the positive nucleus and negative electrons keeps the atom together.

When a gas at low pressure is heated or has a high voltage applied across it, it emits light. If this light is passed through a prism or diffraction grating, it doesn't form a continuous rainbow. Instead, it produces a series of sharp, bright lines of specific colours on a dark background. This is called a line emission spectrum. Conversely, if white light (containing all wavelengths) is passed through a cool sample of the same gas, the resulting spectrum is a continuous rainbow but with dark lines at exactly the same positions as the bright lines in the emission spectrum. This is a line absorption spectrum. These spectra provide direct evidence that electrons in an atom cannot have just any amount of energy. They are restricted to specific, fixed energy values called discrete energy levels. An electron is normally in the lowest possible energy level, known as the ground state. If the atom absorbs energy (e.g., from heat or a collision), an electron can jump up to a higher energy level, an excited state. This state is unstable, and the electron will quickly fall back down to a lower level, emitting the extra energy as a single packet of light, a photon. Because the energy levels are discrete, the energy difference between any two levels is also a fixed value, so the emitted photons have specific energies, corresponding to the specific frequencies and wavelengths seen in the line spectra.

When an electron moves from a higher energy level (E_initial) to a lower energy level (E_final), the atom de-excites and emits a photon. The energy of this photon (E_photon) is precisely the difference between the two energy levels: ΔE = E_initial - E_final. This energy is related to the photon's frequency(f) and wavelength (λ) by the Planck-Einstein relation and the wave speed equation. Energy levels are often given in electron-volts (eV), a convenient unit for atomic physics. 1 eV is the energy gained by an electron when accelerated through a potential difference of 1 volt. When performing calculations using constants like Planck's constant(h) in SI units (Joule-seconds), you must convert energies from eV to Joules (J) using the conversion: 1 eV = 1.60 x 10⁻¹⁹ J.

The Rutherford model was revolutionary, but it had a major flaw. According to classical physics, an orbiting electron is accelerating, and an accelerating charge should continuously radiate electromagnetic energy. This would cause the electron to lose energy and spiral into the nucleus in a fraction of a second, meaning atoms should not be stable. In 1913, Niels Bohr proposed a radical solution for the hydrogen atom that combined classical and early quantum ideas. He made three key postulates:

1. Electrons exist in 'stationary states' (the discrete energy levels) and do not radiate energy while in these stable orbits.
2. An electron can 'jump' between stationary states by absorbing or emitting a photon whose energy is equal to the energy difference between the states.
3. The angular momentum (L) of an electron in a stationary state is quantised. It can only take on integer multiples of a fundamental value, h/2π. The formula is L = mvr = n(h/2π), where 'n' is an integer called the principal quantum number (n = 1, 2, 3, ...), 'm' is the electron mass, 'v' is its speed, 'r' is the orbit radius, and 'h' is Planck's constant.

This third postulate is the most fundamental. By restricting the angular momentum to discrete values, it automatically restricts the possible orbit radii and energy levels to discrete values as well. This quantisation condition provided the theoretical reason *why* the energy levels were discrete and explained why atoms were stable.