Bohr model of the atom

In the ninteenth century, physicists were trying to use atomic spectra to determine the structure of the atom. Hydrogen was studied extensively due to it being the lightest element and having the simplest spectrum. The visible spectrum of H consists of four coloured lines: red, green, blue and purple (see Figure 1). Any theory of the atom that Bohr developed would have to account for these wavelengths.

Figure 1: Visible Spectrum Emmision of Hydrogen
  (1)(2)  (3)                     (4)
|--|--|----|-----------------------|------------|

1. Purple (410nm)
2. Blue (434nm)
3. Green (486nm)
4. Red (656nm)

A valid theory of the structure of the atom would also have to fit the model Rutherford had described, suggesting that electrons orbited the nucleus much as the planets orbit the sun. A serious problem existed with this planetary model, however, in that an electron in an orbit is constantly accelerated towards the nucleus. A simple disproof for the validity of this theory is that if an accelerated electron radiated energy by emitting electromagnetic waves, it would lose energy and spiral into the nucleus in only 10^-9 seconds. From this information, it can be seen that the planetary model is not consistent with the laws of electromagnetism. Also, if the planetary theory was true, the accelerated electron should radiate energy at all wavelengths.

Figure 2: Bohr's Planetary Model of the Atom
     _________
    /  _____  \    n = nucleus
   /  / ___ e- \   e-= electrons
  /  / / n \ \  \
  \  \ \___/ /  /  This diagram would be much easier to follow if it wasn't
   e- \_____/  /   ASCII, I promise. In Bohr's model the orbits are 3D around
    \_________/    the nucleus, but the important thing is that the orbits are
                   fixed around the nucleus (due to Bohr's postulates).

In 1911 Niels Bohr, a Danish physicist, travelled to England and would soon join Rutherford's team to work on the problem of the atom. Bohr started with the planetary arrangement of electrons, but then made the bold hypothesis that the laws of electromagnetism do not operate inside atoms. His first postulate was that an electron in a stable orbit does not radiate energy, even though it is accelerating. Bohr suggested that light was emitted when the electron's energy changed. According to Albert Einstein, the energy of a photon of light is given by the equation E = hf = hc/lambda. Thus, Bohr suggested, if the emission spectrum contains only certain wavelengths, then an electron can only emit or absorb specific amounts of energy; the energy of an electron is quantised.

The atomic electron has different amounts of energy called energy levels. When an electron has the smallest allowable amount of energy it is in its ground state. If the electron absorbs energy, it can make a transmition to a higher energy level. It is then in what is called an excited state. Einstein's theory says that the light photon has an energy hf. Bohr postulated that the change in thae energy of an electron when a photon is absorbed is equal to the energy of the photon, such as:

hf = E_excited - E_ground

When the electron returns to its ground state, a photon is emitted. The energy of the photon is equal to the difference in energy between the ground and excited states of the atom.

An brief overview of Bohr's two postulates and their meanings:

• Electrons have certain "quantised" energy levels
• Radii of electron orbits are also specific values only
• The ground state of an electron is the orbit closest to the nucleus (n=1)
• The excited state of an electron is when an electron in ground receives enough energy to move an orbit further from the nucleus (n>1)
• When an electron moves from an excited state to ground state a photon is emitted, such that hf_photon = E_excited - E_ground

Bohr also proposed a third postulate, stating that the angular momentum - "the product of the momentum of the electron and the radius of its circular orbit", mvr - can only have certain values.

As you would have noticed from the multitude of witty soft-links, Bohr's theory is "Beautiful, but wrong." Ideas such as quantum mechanics, especially the Heisenberg Uncertainty Principle, moved more towards electrons orbiting in a probability cloud instead of exact, circular, quantised orbits.

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Disclaimer: I am not a physicist, but have had this little w/u checked by a few, and even praised by a couple. However, if you do find some stupid mistake, it's my fault; please inform me so I can fix it.