The Bohr Model of the Atom

In the early years of the 20th century, Neils Bohr, a young Danish physicist arrived in Cambridge, England determined to study the structure of atoms. In 1912 he proposed a radical new model that solved the mystery of atomic spectra. Bohr began by studying the spectra of hydrogen, the simplest of elements. In 1912 physicists already understood that hydrogen consisted of a single negatively-charged electron flying around a single positively-charged proton at the atom's center (the nucleus). That, however, was about all they knew. The structure of hydrogen and other atoms were shrouded in a cloud of mystery. The location and motion of the electron, as well as its role in emitting and absorbing light was still completely unclear. Every atomic model physicists tried had failed in one way or another. Then came Bohr.

Bohr imagined that the proton in a hydrogen atom was surrounded by distinct electron orbits. These were like circular tracks around nucleus that guided the electrons motion. What made Bohr's model so radical was he assumed that the orbits were "quantized", meaning there were orbital paths only at certain locations. There might be an orbit with a radius (a distance from the proton) of .1 nanometer and another with a radius of .4 nanometers but never one in between. It was a big leap.

In Bohr's model there was a relationship between the energy of an electron's orbits and their radius. Since the orbits are quantized, they could be labeled n = 1, 2, 3..., with the electron getting farther from the proton as n gets bigger. When the electron was in some particular orbit, which we'll call the "n-th" orbit, Bohr found the energy which binds (glues) it to the proton was

where E₁ was the energy of the smallest orbit (also called the ground state). In words this formula says the energy of the n-th orbit equals the energy of the first orbit divided by the orbit's radius squared. Notice how the "binding" energy of each orbit is directly related to its distance from the nucleus. Thus, the energy of an orbit gets closer to zero the farther the electron is from the proton. This way of defining binding energy means higher orbits (more distant ones) have less binding energy. A zero binding energy would mean the electron was freed from the proton and could wander around on its own.

With this model of the atom, Bohr was able to explain why hydrogen had its strange emission and absorption line spectra.

Bohr proposed that if an electron were in a big orbit (n is large) it could spontaneously "jump" down to a lower orbit. By "falling" closer to the proton, the electron would give off energy in the form of a light particle (called a photon). Since there was only a very clearly defined and definite set of possible orbits, the number of possible downward jumps by an electron was cast in stone. That meant the energy of the emitted photons was also set. In a formula the idea looks like this

This equation says the energy of the emitted photon is equal to the difference in energy between the higher orbit the electron started in and the lower one it jumped down into. Recall that emission-line spectra only showed light at certain wavelengths. How did Bohr?s model translate into predictions for the wavelengths? Physicists (like Einstein) had already shown that there was a relationship between the energy of a photon and its wavelength

where the Greek symbol "lambda" (l ) is the wavelength of the light measured in Nanometers (nm) and eV stands for Electron Volts which is a unit of energy (so eV - nm or "electron volt - nanometers" are the units on the equation). In words this equation says the energy of the emitted photon is 1240 electron volt - nanometers divided by the photons wavelength. According to the equation, red light (which has a long wavelength) must have a relatively low energy and blue light (which has a short wavelength) must have relatively high energy.

In Bohr?s model the energy the electron gives up by jumping from one orbit to the other should equal the energy of the emitted photon (E_jump = E_photon). With a little algebra you can see the relationship between the energy of the orbit jump and the emitted photon?s wavelength.

So the wavelength of the emitted photon must equal 1240 electron volt - nanometers divided by the orbit's energy difference. What was amazing about this formula is it exactly predicted all the wavelengths of emission lines in the hydrogen atom.

Absorption-line spectra were now also easy to explain. Imagine a hydrogen atom where bathed in light from the outside and that light had photons of all different wavelengths in it (i.e. a rainbow). In Bohr's model an electron in a lower orbit could jump to a higher orbit by absorbing an incoming photon of just the right energy (i.e. wavelength). The "quantum jumps" to higher orbits via photon absorption are what give absorption spectra the appearance of a rainbow pattern with dark lines "bitten" out of them.

It?s hard to overstate just how important Bohr?s achievement was. He had successfully explained the strange patterns in both emission and absorption spectra and had created the first working model for the structure of the atom. Bohr became a leader in a revolution that ushered in the new field of "quantum physics", the study of the micro-world. Much of the basis for atomic and sub-atomic physics came from Bohr?s insight. It was a huge achievement but it came at the cost of abandoning some degree of "common sense" intuition. In Bohr?s model of the atom the electron can never exist in any location other than its pre-defined orbits. Even when it jumps it "disappears" from one orbit and reappears in the other without ever occupying the space in-between. It is like crossing a room by popping into and out of a few distinct locations but never touching the spaces in-between.