The way X-ray spectroscopy works depends on the atom's electrons rather than its protons. The light each element emits when its atoms are excited creates a specific spectrum, filled with special absorption lines called Fraunhofer lines. You can tell a lot from these lines and they are invaluable for studying the compositions of faraway stars simply by examining their light. These lines are present in every spectrum, even the band of colours you see in a prism or a rainbow. You don't usually see them because they are extremely fine. Each line is created by electrons in atoms absorbing photons of a very specific energy, observed as a specific wavelength of electromagnetic radiation, or colour.
The Sun's visual spectrum with Fraunhofer lines is shown below.
When an atom is excited (has extra energy), one or more electrons jump up to higher energy orbitals. An electron can gain energy by absorbing a photon of a specific energy or by absorbing energy through a collision with another particle such as an electron. The atom's electron then releases the extra energy as a photon of a specific wavelength when it jumps back down to its non-excited state. Absorption and emission give each element an absorption spectrum and an emission spectrum. Simplified spectra of hydrogen are shown below.
As often happens in science, a breakthrough begins with a problem. In 1913, Niels Bohr (shown below right) proposed a solution to a very disturbing problem with Rutherford's atomic model.
Larmor formula specifically), an electron should release electromagnetic (EM) radiation while orbiting a nucleus because the electron is in a state of acceleration so it should continuously lose energy and spiral inward, and all the while the frequency of the EM radiation should increase. This means that no atom can be stable. Bohr, thinking about this, proposed that electrons orbit only in stable orbits around the nucleus which are set at specific energies and which don't change. They orbit as different frequencies of standing waves in other words. These waves have resonance so the continuing waves interfere constructively with each other, maintaining the energy of each electron in its orbit.
Below is a typical Bohr model of an atom; this one is an excited hydrogen atom. It has just one electron, which can assume one of many different possible energy levels, some of which are represented below as grey circles. These circles represent electron energy shells. Higher shells represent more energy (hydrogen has more than 11 energy shells, which are increasingly faint in its spectrum because these electron transitions are increasingly rare events).
The Bohr model was not only about to help usher in a huge breakthrough in atomic theory - quantum mechanics - it also had great bonus effects - it explained why Rydberg's formula works and it sparked a way to figure out why atomic number corresponds to proton number in the periodic table.
Henry Moseley, a physicist (shown below), became interested in Bohr's new atomic model. Moseley knew that Rydberg's formula worked very well for hydrogen, but he wanted to know if it also worked for larger atoms as well. He also wanted to know if there was a real physical relationship between atomic number and atomic weight.
To explore his questions, Moseley studied the brightest spectral line (called the K-alpha line) of ten elements from calcium (Z=20) to zinc (Z=30). This spectral line is the result of a transition by a single electron from an outer L (also called n=2) electron energy shell to an inner K (also called n=1) shell of the atom.
When an electron jumps down from the L shell to the K shell, it emits photon of a particular X-ray frequency (the K-alpha line). We know today that the wavelength of the K-alpha line depends on the energy of the electron's energy shells. The energy of an electron's energy shell depends on a complex interaction between two opposing forces - electrostatic repulsion between the electron and all other electrons in the atom, which depends on where the electrons are located relative to each other, and second, the electrostatic attraction between the electron and the nucleus, which depends on how much positive charge (how many protons) the nucleus has. Shielding by the nucleus also complicates matters because there is always at least one electron that is opposite the electron in question, with its repulsive charge being shielded by the charge of the nucleus. This complex picture is why the Rydberg formula only works perfectly for hydrogen (a simple arrangement of an electron and a proton) and well for elements that have small nuclei and few electrons, such as the ions He+, Li2+ and Be3+ with reduced numbers of electrons.
Moseley found a way to identify larger elements by developing a formula (Moseley's law) from his work with larger (calcium to zinc) atoms. This formula can be used to predict the strongest spectral line, the K-alpha (n=2 to n=1emission) line, for larger atoms. These atoms, despite their complexity, have one trend in common that makes Moseley's law work. As the charge of the nucleus increases, the attractive pull on electrons in the closest energy shell increases in a fairly simple linear way. A photographic recording of his results is shown below left.
As nuclear size increases, more energy is required to move electrons up from the n=1 shell to the n=2 energy shell farther away from the positive charge, and therefore more energy (a shorter X-ray wavelength) is emitted when that electron falls back down to n=1.
Moseley found a systematic relationship between wavelength and the element's atomic number, providing a physical basis for a number that, before this, was considered to be more or less an arbitrary place setting for elements listed according to their increasing atomic weights. An example of how Moseley's work is useful comes from comparing cobalt (top) and nickel (bottom) shown below right.
X-ray spectroscopy is also a very useful tool for distinguishing elements that are almost identical chemically and physically. For example, its use proved the existence of a missing element predicted at atomic number 72, hafnium. This element is chemically virtually indistinguishable from zirconium, Z=40) and they are often found in the same mineral. Hafnium (top) and zirconium (bottom) are shown below left.
In 1913, Moseley concluded not only that atomic number was the most important factor in ordering the periodic table, but that this ordering was more consistent with the chemical and physical properties of elements than atomic weight was.
In this model, the energy and position of electrons inside an atom are determined by a set of numbers called quantum numbers, and it changed our mental picture of an electron from a particle/wave to a fuzzy cloud. The numbers are solutions to complex quantum equations. They not only define the electron's energy state but also the shape of its trajectory, or orbital, when it is in that energy state.
Around 1925, Erwin Schrodinger applied the principles of wave mechanics to the atom. His solutions resulted in various orbital shapes for electrons based on their energies. In the same year, Werner Heisenberg applied his quantum uncertainty principle to the electron, defining orbitals further as probability densities, and refining the electron itself into a fuzzy cloud of charge rather than a particle/wave.
An online chemistry lecture called Atomic Theory: The Quantum Model of the Atom from the University of Vermont provides an excellent review of the evolution of atomic theory described in this article.
Next up: History of the Periodic Table Part 4.