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Bohr’s Model of Atom

BOHR’S MODEL OF ATOM 

In order to overcome the shortcomings of Rutherford’s model, of atom Bohr (19 13) proposed a new model of atom based upon quantum theory of radiations.

Main points of this model are:

1. The electrons in an atom revolve around the nucleus only in certain selected circular orbits. These orbits are associated with definite energies and are called energy shells or energy levels. These are numbered as 1, 2, 3, 4 …… etc., or designated as

K, L, M, N . ….. , etc., shells (Fig. 5.18).

The energy of the electron is minimum in the orbit nearest to the nucleus i.e., K shell. The energy of the electron increases as it moves away from the nucleus. Electron in a particular orbit remains constant. That is why, these orbits are also called stationary states.

3. When energy from some external source is supplied to the electron, it may jump to some higher energy level by absorbing a definite amount of energy (equal to the difference in energy between th.e two energy levels). When the electron jumps back to the lower energy level it radiates the difference in energy in the form of a photon of electromagnetic radiation.

 

DISTRIBUTION OF ELECTRONS IN ENERGY SHELLS

As already mentioned electrons in an atom revolve around the nucleus in well defined circular orbits or energy shells. Let us now study how electrons are distributed in energy shells of an atom.

The arrangement of electrons in various energy levels of an atom is known as the electronic configuration of the atom. While writing the electronic configuration the following rules as given by Bohr and Bury are followed:

1. Electrons fill up the lowest energy levels first.

2. The maximum number of electrons in any orbit is given by the formula 2n2 where n is the number of the orbit.

For example,

For the first orbit (n = 1), the maximum number of

electrons = 2 x ( l)2 = 2

For the second orbit (n = 2), the maximum number of

electrons = 2 x (2)2 = 8

For the third orbit (n = 3), the maximum number of

electrons = 2 x (3)2 = 18

3. The outermost orbit in a stable atom cannot have more than 8 electrons even if it can accommodate more electrons according to rule 2.

4. The penultimate energy shell, i.e., the energy shell preceeding the outermost shell, cannot have more than 18 electrons.

Let us apply the above rules to write electron distribution about the nucleus in some elements.

I. Case of Hydrogen Atom

Atomic number of hydrogen is 1. There is only one electron in hydrogen atom which goes into the lowest energy shell i.e. , K shell. Thus, the electronic configuration of hydrogen atom is:

  Fig. 5.19. Hydrogen atom

H: K

1

Atomic diagram of hydrogen atom is shown in Fig. 5.19.

Here, symbol of the element represents the nucleus and the circle drawn around the symbol represents the first energy shell. The dot in the ring represents the electron.

II . Case of Oxygen Atom

Now consider an atom of oxygen. Atomic number of oxygen is 8. Thus, there are eight electrons in an atom of oxygen. Two electrons are accommodated in the first shell (K shell) and the remaining six electrons are accommodated in second shell (L shell).

   Fig. 5.20. Oxygen atom

O: K, L

2 6

The atomic diagram of oxygen is shown in Fig. 5.20. 

III. Case of Calcium Atom

Atomic number of calcium is 20. An atom of calcium contains 20 electrons. 2 electrons go in the first shell (K shell), 8 electrons go to the second shell (L shell), next 8 electrons go to the third shell (M shell) and the remaining 2 electrons go to the fourth shell (N shell). Although the third shell can accommodate a maximum of 1 8 Fig. 5.2.1 . Atomic electrons, all the 10 electrons cannot diagram’ of calcium . go into it because that would make 1 0 electrons in the outermost shell whereas the outermost shell cannot have more than 8 electrons. After the third level acquires 8 electrons, the fourth level begins to ftll. The next 2 electrons go to the fourth energy shell (N shell)

Ca: K   L    M   N

2   8     8   2

SUCCESSES OF BOHR’S MODEL 

The main successes of Bohr’s model are:

1. Bohr’s model could explain the stability of an atom. According to Bohr’s model, an electron revolving in a particular orbit cannot lose energy. The electron can lose energy only if it jumps to some lower energy level. If no lower energy level is vacant then electron will keep on revolving in the same orbit without losing energy and hence it explains the stability of atom.

2. Bohr’s theory helped in calculating energy of an electron in a particular orbit of hydrogen.

3. Bohr ‘s model could explain the atomic spectrum of hydrogen.

According to Bohr’s model, electron in an atom can have only certain definite energy levels. When the electron is  present in lowest possible energy level, it is said to be in ground state. When energy is supplied from some external source, the electron may absorb energy and jump to some higher energy level. The electron in such a state is said to be in excited state. The excited state is unstable and, therefore, the electron has tendency to come back to the ground state. When the electron jumps back to lower energy levels, it gives out energy in the form of a quantum equal to the difference of energies between the two energy levels. If E1 and E2 are the energies of lower and higher energy levels respectively, then frequency (v) of the radiation emitted is given by the following relation:

E2– E1 = hv   or    v = E2 –E1 /h

where h is Planck’s constant.

According to Bohr’s model, in a hydrogen atom (or in any other atom) E2 and E1 can have only certain definite values. From this, it follows that v can have only certain fixed values. Thus, Bohr’s model explains why there are certain discrete lines in the spectrum of hydrogen.

The lines which arise due to the transitions from hi her  energy levels to first energy level are grouped as Lyman series. Similarly, the lines obtained as a result of transitions of electrons from higher energy levels to second, third, fourth and fifth energy levels give rise to Balmer, Paschen, Brackett and Pfund series respectively as illustrated in Fig. 5.22.

Fig. 5.22. Generation of various spectral

    series in hydrogen spectrum.

LIMITATIONS OF THE BOHR’S MODEL

Bohr’s theory could explain successfully the positions of various series of lines in the hydrogen spectrum but could not explain the spectra of atoms containing more than one

electron. Bohr’s model could not explain even hydrogen spectrum obtained using high resolution spectroscopes. Each spectral line, on high resolution, was found to consist of two closely spaced lines.

It was observed that in the presence of a magnetic field, each spectral line gets split up into closely spaced lines. This phenomenon, known as Zeeman effect, could not be explained by Bohr’s model.

In order to overcome the limitations of the Bohr’s model, attempts were made to develop a more suitable and general model for atoms. The two new concepts which led to development of such a model were:

1. The dual behaviour of matter.

2. Heisenberg’s uncertainty principle.