Bohr's Atomic Model - Kailasha Online Learning LLP

Bohr developed a model of an atom by modifying Rutherford’s model of an atom. The important postulates given were:

An atom consists of a dense nucleus situated at the centre with the electron revolving around it in circular orbits without emitting any energy.
The force of attraction between the nucleus and an electron is equal to the centrifugal force of the moving electron.
The permitted angular momentum (mvr) in electron orbit is integral multiple h/2π.

i.e. mvr = nh/2π.

Where, m = mass of electron, v = velocity of electron, n = orbitnumber in which electron is present, r = radius of the orbit, h = Planck’s constant.

An electron neither lose nor gain energy while revolving in an orbit. Since, there is no energy loss or gain, so these are called stationary orbits.
Each stationary orbit has a fixed definite amount of energy and these stationary orbits are also called energy levels. The greater is the distance of orbit from the nucleus, more is the energy associated with it. These energy levels are numbered as 1, 2, 3 4 (1 is nearest to the nucleus) or K, L, M, N etc.
In the stable state of an atom, electron continues to move in a particular orbit without losing any energy.
If energy is supplied to electrons in any form, the electron jumps from the lower energy level to higher energy level by absorbing one or more quanta of energy. When electrons are in higher energy state then the atom is said to be in an excited state. The energy of quanta absorbed is equal to the difference in the energy of the two levels in which transition occurs.
Excited states are less stable and hence electron always jumps back to the ground state by releasing the energy.

Energy absorbed or released in an electron jump, (∆E) is given by

∆E = E₂ – E₁ =hν

Where E₁and E₂are the energies of the electron in the first and second orbit or energy level and ν will be the frequency of radiation absorbed or released.

Radius of Atom using Bohr Model:

Let us consider an electron having mass ‘m’ and charge ‘e’ is revolving around a nucleus having atomic number Z with tangential velocity v. So charge in the nucleus will be Ze (e is the charge of the proton).

As per Coulomb’s Law, the electrostatic force of attraction between electron and nucleus will be given by

Energy of electron in nth orbit

The energy of an electron at any time in an atom will be the sum of its kinetic energy as well its potential energy.

Now, the Kinetic energy of the electron will be given by (1/2)mv²

Hydrogen spectrum by Bohr’s theory

As per Bohr’s atomic theory electron neither emits nor absorbs energy, as long as it stays in a particular orbit. However, when an atom absorbs energy, the electron in the atom may jump from the ground state to some higher energy level i.e., exited state.

But as the life time of the electron in the excited state is short, it returns to the ground state in one or more jumps.

During each jump, energy is emitted in the form of a photon of light of definite wavelength or frequency. The frequency of the photon of light thus emitted depends upon the energy difference of the two energy levels concerned (n₁, n₂), and the frequency is given by

Achievement of Bohr’s Theory

(i) The experimental value of radius and energy of hydrogen atom were good in agreement with that calculated with Bohr’s theory.

(ii) Bohr’s model was able to explain the emission and absorption spectra of hydrogen and hydrogen like an atom.

Limitations of Bohr Model of Atom

(i) Bohr’s model was unable to explain the spectrum of atoms having more than one electron in their orbit.

(ii) Bohr’s model was unable to explain the Zeeman (Splitting of the spectral line into several component by the application of magnetic field) and Stark effect (Splitting of the spectral line into several component by the application of electric field).

(iii) Dual character of electron suggested by De Broglie was not considered in Bohr’s model of an atom.

(iv) TheHeisenberg’s Uncertainty Principle contradicts the Bohr’s postulate that “electrons revolve in well-defined orbits around the nucleus with well-defined velocities”.