Niels Bohr proposed a model for the hydrogen atom that explained the spectrum of the hydrogen atom. The Bohr model was based on the following assumptions.

- The electron in a hydrogen atom travels around the nucleus in a circular orbit.
- The energy of the electron in an orbit is proportional to its distance from the nucleus. The further the electron is from the nucleus, the more energy it has.
- As long as the electron stays in a stationary orbit (same distance from the nucleus), it does not emit radiation as classical physics required.
- Only a limited number of orbits with certain energies are allowed. This is the quantization of orbits using Planck's hypothesis. Allowed orbits have their electron's angular momentum be an integral multiple of Planck's constant divided by 2pi.
- An electron can only pass from one stationary state to another. Radiation is absorbed when an electron jumps to a higher energy orbit and emitted when an electron falls into a lower energy orbit.
- The energy of the radiation emitted or absorbed is exactly equal to the difference between the energies of the orbits.

Here is a good site for a more detailed development of the Bohr theory of the atom. This site also has two problems for you to practice.

Using the above assumptions, the energy of a hydrogen atom in level n was found to be

E = -R_{H}/n^{2} where R_{H} = 2.179 x 10^{-18}

We can then calculate the change in energy when an electron changes from n=3 to n=2

E = E_{3} - E_{2}
= (--R_{H}/3^{2}) - (--R_{H}/2^{2}) or

E = -R_{H}(1/2^{2} - 1/3^{2})
which also must be equal to h*.

Solving for gives

= E/h = R_{H}/h * (1/2^{2} - 1/3^{2}) which gives

R_{H}/h = 2.179 c 10^{-18}J/6.626 x 10^{-34}Js or

R_{H}/h = 3.289 x 10^{15}s^{-1}

This is within experimental error of the constant in the Balmer equation for a hydrogen transition series (3.2881 x 10^{15}s^{-1}) which really made everyone take notice.

Go here to obtain further insight into the Bohr model of the atom. Be sure to click on "Next" at the bottom of this site to continue with the explanations.

However, the Bohr model

- Could not account for the spectra of anything other than hydrogen.
- Could not account for the ability of atoms to form molecules.

People tried modifying the theory by allowing the electrons to have elliptical orbits and other changes, but when you have a bad model you need to start over and that is what we will do next.

Now take a practice quiz to help you understand if you understand the basic concepts. |

You must use your real name when it asks for a name. |

The test will only submit when you have answers all of the questions correctly. |

If you are not taking this course for credit please do not answer all the questions correctly for I don't want to be flooded with email answers to the tests. |