The first modern picture of an atom was put forward by Rutherford in 1911. Such an atom has a central nucleus of small dimension around which move a number of electrons. The electron orbits are of atomic dimensions i.e. of the order of 10^-8 cm. The nucleus carries a charge to counteract the combined charge of the electrons. Almost the whole of the mass of the atom resides in the nucleus. The Rutherford's model of the hydrogen atom is shown in Fig 1.4.

The hydrogen atom consists of a proton and an electron revolving round the nucleus in an orbit of radius r. The electron in the circular orbit experiences centripetal acceleration. According to electromagnetic theory such an electron must radiate energy in the form of electromagnetic waves. The total energy of the electron in any orbit is the sum of its kinetic and potential energies. The potential energy of an electron is considered to be zero when it is an infinite distance from the nucleus. The relation between the total energy possessed by an electron W and the radius of the circular orbit  r can be represented as follows:-

Total energy (W) = potential energy + kinetic energy

Where

Z is the atomic number (=1 for Hydrogen)

q is the charge of an electron

=(1.6 x 10 ^{- 9} coulomb)

And e _o is the permittivity of free space

=(8.854 x 10 ^{- 12} farad / meter)

The main drawbacks of the Rutherford model are:-

If the accelerated electrons lose energy by radiation, the total energy must fall and the electron must spiral into the nucleus. Thus an atom cannot be stable. But most atoms are stable.

According to classical electromagnetic theory, an accelerating electron must radiate energy at a frequency equal to the mechanical frequency of the orbiting electron. This means that as the electron spirals towards the nucleus its angular velocity tends to infinity. This will result in a continuous spectrum. But it has been observed that many atoms like hydrogen emit line spectra of fixed wavelengths only.