Electrons Can Behave as Waves: The Quantum Model of the Atom
Although the Bohr model adequately explained how atomic spectra worked, there were several problems that bothered physicists and chemists:
Obviously, the Bohr model was missing something!
- Why should electrons be confined to only specified energy levels?
- Why don't electrons give off light all of the time?
- As electrons change direction in their circular orbits (i.e., accelerate), they should give off light.
- The Bohr model could explain the spectra of atoms with one electron in the outer shell very well, but was not very good for those with more than one electron in the outer shell.
- Why could only two electrons fit in the first shell and why eight electrons in each shell after that? What was so special about two and eight?
In 1924, a French physicist named Louis de Broglie suggested that, like light, electrons could act as both particles and waves (see De Broglie Phase Wave Animation for details). De Broglie's hypothesis was soon confirmed in experiments that showed electron beams could be diffracted or bent as they passed through a slit much like light could. So, the waves produced by an electron confined in its orbit about the nucleus sets up a standing wave of specific wavelength, energy and frequency (i.e., Bohr's energy levels) much like a guitar string sets up a standing wave when plucked.
Another question quickly followed de Broglie's idea. If an electron traveled as a wave, could you locate the precise position of the electron within the wave? A German physicist, Werner Heisenberg, answered no in what he called the uncertainty principle:
We can never know both the momentum and position of an electron in an atom. Therefore, Heisenberg said that we shouldn't view electrons as moving in well-defined orbits about the nucleus!
- To view an electron in its orbit, you must shine a wavelength of light on it that is smaller than the electron's wavelength.
- This small wavelength of light has a high energy.
- The electron will absorb that energy.
- The absorbed energy will change the electron's position.
With de Broglie's hypothesis and Heisenberg's uncertainty principle in mind, an Austrian physicist named Erwin Schrodinger derived a set of equations or wave functions in 1926 for electrons. According to Schrodinger, electrons confined in their orbits would set up standing waves and you could describe only the probability of where an electron could be. The distributions of these probabilities formed regions of space about the nucleus were called orbitals. Orbitals could be described as electron density clouds (see Atomic & Molecular Orbitals for a look at various orbitals). The densest area of the cloud is where you have the greatest probability of finding the electron and the least dense area is where you have the lowest probability of finding the electron.
The wave function of each electron can be described as a set of three quantum numbers:
It was later suggested that no two electrons could be in the exact same state, so a fourth quantum number was added. This number was related to the direction that the electron spins while it is moving in its orbit (i.e., clockwise, counterclockwise). Only two electrons could share the same orbital, one spinning clockwise and the other spinning counterclockwise.
- Principal number (n) - describes the energy level.
- Altazimuth number (l) - how fast the electron moves in its orbit (angular momentum); like how fast a CD spins (rpm). This is related to the shape of the orbital.
- Magnetic (m) - its orientation in space.
The orbitals had different shapes and maximum numbers at any level:
The names of the orbitals came from names of atomic spectral features before quantum mechanics was formally invented. Each orbital can hold only two electrons. Also, the orbitals have a specific order of filling, generally:
- s (sharp) - spherical (max = 1)
- p (principal) - dumb-bell shaped (max = 3)
- d (diffuse) - four-lobe-shaped (max = 5)
- f (fundamental) - six-lobe shaped (max = 7)
However, there is some overlap (any chemistry textbook has the details).
The resulting model of the atom is called the quantum model of the atom.