Bohr’s theory of the hydrogen atom
The Rutherford model of the atom and the experimental formula of atomic spectra helped Bohr is solving the problem of atomic structure.In 1913 he proposed a model for the structure of a hydrogen atom based on his experimental observations.
Bohr atomic model postulates
Neil Bohr based his theory of hydrogen atom on the following three postulates.
The postulates of stationary states
Bohr assumed that hydrogen atom can exist for a long time without radiating in any one of the numbers of stationary states of well-defined energy.
Angular momentum postulate
Only those orbits around the nucleus are possible for which angular momentum is the integral multiple of h/2π i.e:
In other words orbits are quantized.
The frequency postulate
Bohr assumed that hydrogen atom can emit or absorb radiation only when the atom changes from one of its stationary states to another.If an atom changes from initial state of energy En to a final state of lower energy Em, then the energy of the emitted photon is given by:
hν = En -Em ——————–(1)
Derivation of Bohr’s theory
The hydrogen atom is the simplest of the atoms because it contains only one proton in its nucleus and one electron revolving around it in the first orbit.We take central charge to be ‘Ze’ where ‘Z’ is the atomic number and z=1 for the hydrogen atom.Suppose M is the nuclear mass and me is the mass of an electron.The force of attraction between the nucleus and the electron provides centripetal force to the electron to move in circular orbit.Hence we can write: