Structure of Atom
7.0 Bohr’s Atomic Model
7.0 Bohr’s Atomic Model
In 1913, Niels Bohr (1885-1962) proposed a model of the atom where electrons move around the nucleus in circular paths.
Bohr’s atomic model is built upon a set of postulates, which are as follows :
1. The electrons move in a definite circular paths around the nucleus, called as orbits and postulated that as long as the electron is in a given orbit its energy does not change (or energy remains fixed). These orbits were therefore referred to as stationary orbits or stationary states or non radiating orbits.
2. The electron can change its orbit by absorbing or releasing energy. An electron at a lower (initial) state of energy, $E_i$ can go to a (final) higher state of energy, $E_f$ by absorbing a single photon of energy given by, $$E = h{\nu _o} = {E_f} - {E_i}$$
When electron changes its orbit from a higher initial state of energy $E_i$ to a lower final state of energy Ef , a single photon of energy h? is released.
3. The angular momentum of an electron of mass m moving in a circular orbit of radius r and
velocity v is an integral multiple of h/2$\pi $
$$mvr = \frac{{nh}}{{2\pi }}$$
where n is a positive integer, known as the principal quantum number.
Bohr obtained the following expressions for the energy of an electron in stationary states by using his postulates :
$${E_n} = - 2.178 \times {10^{ - 18}}\frac{{{Z^2}}}{{{n^2}}}J$$
$${E_n} = - 13.6 \frac{{{Z^2}}}{{{n^2}}}eV$$
The negative sign in the energy expression means that the there is an attractive interaction between the nucleus and the electron. This means that certain amount of energy (called
ionisation energy) would be required to remove the electron from the influence of the nucleus in the atom.
Velocity of an Electron in nth Bohr Orbit
$${v_n} = 2.165 \times {10^6}\frac{Z}{n}m/s$$
Radius of nth Bohr Orbit
$${r_n} = 0.53\frac{{{n^2}}}{Z}\mathop {\text{A}}\limits^ \circ $$
