The Rutherford nuclear atom stated that electrons were in constant motion around a nucleus, either that or they would be pulled into the nucleus by the attraction between opposite charges. He suggested that electrons might orbit the nucleus as planets orbit the sun. But, electrons are charged, planets are not, and it was predicted that charged particles moving in circles should emit radiation. As a result, the electrons would very quickly radiate away all of their energy and spiral into the nucleus.

In 1913 Niels Bohr made the following three assumptions:-

1. The electron in the hydrogen atom can move about the nucleus in any one of several fixed circular orbits, but only in these orbits.

2. The angular momentum of the electron in a hydrogen atom is quantised; it is a whole number multiple of h / 2p . This is why only certain fixed orbitals are allowed. Angular momentum, which is given by mass x velocity x the radius of a body's motion, is a measure of the tendency of a body to keep moving on a curved path.

For an electron in a Bohr atom:

m u r = n (h / 2p )

mass of e^- x velocity x radius of Bohr orbital = quantum number (Planck's constant / 2p )

It can be shown that an electron, assigned an energy for each orbit, is governed by:

E µ m e⁴ / n²

energy = mass of e^- x charge of e^- / quantum number

No energies other than those determined by this equation are possible. The lowest energy orbit in an atom is called the ground state. The states of energy higher than the ground state are excited states, reached by the electrons when the atom has absorbed extra energy.

3. The electron does not radiate energy as long as it remains in one of the orbits

Quantum Number or n in the above equations is a whole number multiplier that specifies an amount of energy. An electron in a Bohr atom would have wave-like motion.

The allowable wavelengths are given by the expression;

l = 2p r / n

otherwise the wave would interfere with itself and cancel itself out.

Information provided by: http://www.bpx.cov.ac.uk