Bohr’s Model For Hydrogen Atom

Presented by-

P. Deepak Kumar

Overview of presentation

• Bohr’s atomic model

• Postulates of Bohr’s atomic model

• Successes of Bohr’s model

• Calculations based on Bohr’s model

• Limitations of Bohr’s Model

• Bibliography

Bohr’s Atomic Model

• An atom is made up of three particles, electrons, protons and neutrons. Electrons have a negative charge and protons have a positive charge whereas neutrons have no charge. They are neutral. Due to the presence of equal number of negative electrons and positive protons, the atom as a whole is electrically neutral.

• The protons and electrons are located in a small nucleus at the centre of the atom. Due to the presence of protons, the nucleus is positively charged.

• The electrons revolve rapidly around the nucleus in fixed circular paths called energy levels or shells. The 'energy levels' or 'shells' or 'orbits' are represented in two ways: either by the numbers 1, 2, 3, 4, 5 and 6 or by letters K, L, M, N, O and P. The energy levels are counted from centre outwards.

• Each energy level is associated with a fixed amount of energy. The shell nearest to the nucleus has minimum energy and the shell farthest from the nucleus has maximum energy.

• There is no change in the energy of electrons as long as they keep revolving with the same energy level. But, when an electron jumps from a lower energy level to a higher one, some energy is absorbed while some energy is emitted.

• When an electron jumps from a higher energy level to a lower one, the amount of energy absorbed or emitted is given by the difference of energies associated with the two levels. Thus, if an electron jumps from orbit 1 (energy E1) to orbit 2 (energy E2), the change in energy is given by E2 - E1.

• The energy change is accompanied by absorption of radiation energy of E = E2 E1 = h where, h is a constant called 'Planck's constant' and is the frequency of radiation absorbed or emitted. The value of h is 6.626 x 10-34 J-s. The absorption and emission of light due to electron jumps are measured by use of spectrometers.

Postulates of Bohr’s Atomic Model

• Electrons revolve round the nucleus with definite velocities in concentric circular orbits situated at definite distances from the nucleus. The energy of an electron in a certain orbit remains constant. As long as it remains in that orbit, it neither emits nor absorbs energy. These are termed stationary states or main energy states.

• Bohr proposed that the angular momentum of an electron is quantized. Thus, the motion of an electron is restricted to those orbits where its angular momentum is an integral multiple of h/2π, where h is Planck’s constant.

• Thus we have the relationship mvr = nh/2π, where m is mass of electron, v is velocity of electron of said orbit, r is radius of that orbit, n is a simple integer.

• The stationary states or allowed energy levels are only those where n = 1, 2, 3, …… This is called Bohr quantum condition.

• The energy of an electron changes only when it moves from one orbit to another. An electronic transition from an inner orbit to outer orbit involves absorption of energy. Similarly, when an electron jumps from an outer orbit to inner orbit it releases energy, which is equal to the difference between the two energy levels.

• The energy thus released in the form of a radiation of a certain frequency appears in the form a line in the atomic spectrum. If the energy of an electron in the outer orbit (n2) is E2 and energy of electron in the inner orbit (n1) is E1 then E2 - E1 = ΔE = hν.

• The value of n could be small integers 1, 2, 3 and these correspond to the first, second, third, and so on. Quantum states are shells for the electron; n is termed as principal quantum number.

• Based on the Bohr theory ,Bohr calculated the radii of the various orbits and the energies associated with the electrons present in those shells.

Successes of Bohr’s Model

• When electron jumps from lower energy level to higher energy level, it absorbs relevant amount of energy and this results in the absorption spectrum.

• When an electron drops to higher level from lower level, it emits some amount of energy and emission spectrum is observed.

• Since there is only one electron in hydrogen atom, there should be one line in hydrogen spectrum. But in Bohr theory, there are infinite number of orbits, so more than one line is observed in spectrum.

Calculations based on Bohr’s Model

• Radius of nth orbitAccording to bohr model, the attraction force between electron and nucleus is balanced by centrifugal force of electron which is due to motion of electron and tend to take electron away from nucleus.

• Since the value of Z is constant for an atom, r n α n2 , so radius increases with increasing the value of n.

• If the value of n is constant , rn α 1/Z

• Hence, radius of a particular orbit decreases with increasing the atomic number.

• Energy of electron in nth orbit

According to Bohr atomic model, the maximum energy value of electron at infinite is zero because of negligible attraction force between electron and nucleus at infinite distance.

Hence, as electron comes closer to nucleus, the energy becomes negative.

Limitations of Bohr’s Model

• Bohr model could not explain those atoms which have more than one electron like lithium, helium. This model was applicable only for those atoms which have one electron.

• Bohr theory explained only spherical orbits. There was no explanation for elliptical orbits.

• This model failed to explain Zeeman Effect and stark effect.

• Bohr model could not explain the uncertainty principle of Heisenberg.

• Bohr model was not related with classification and periodicity of elements.

• By using Bohr atomic model, one can’t explain the intensity of spectrum line.

• Bohr model could not explain the wave nature of electron. It explained only particle nature of electron.

Bibliography

• Physical Chemistry, Part-1 by Dr. K.S. Verma

• http://en.wikipedia.org/wiki/history of atomic theory

Thanks for your kind attention