for the stability and line spectra of hydrogen atom and hydrogen like ions (for example, He + , Li + , Be + , and so on). However, Bohr’s model was too simple to account for the following points. i) It fails to account for the finer details (doublet, that is two closely spaced lines) of the hydrogen atom spectrum observed by using sophisticated spectroscopic techniques. This model is also unable to explain the spectrum of atoms other than hydrogen, for example, helium atom which possesses only two electrons.
Further, Bohr’s theory was also unable to explain the splitting of spectral lines in the presence of magnetic field (Zeeman effect) or an electric field (Stark effect). ii) It could not explain the ability of atoms to form molecules by chemical bonds. In other words, taking into account the points mentioned above, one needs a better theory which can explain the salient features of the structure of complex atoms. .
Towards Quantum Mechanical Model of the Atom In view of the shortcoming of the Bohr’s model, attempts were made to develop a more suitable and general model for atoms. Two important developments which contributed significantly in the formulation of such a model were: . Dual behaviour of matter, . Heisenberg uncertainty principle.
. . Dual Behaviour of Matter The French physicist, de Broglie, in proposed that matter, like radiation, should also exhibit dual behaviour i.e., both particle and wavelike properties. This means that just as the photon has momentum as well as wavelength, electrons should also have momentum as well as wavelength, de Broglie, from this analogy, gave the following relation between wavelength ( λ ) and momentum (p) of a material particle.
According to de Brogile equation ( . ) h m v Js kg m s ( . ) ( . )( ) = .
× – m (J = kg m s – ) Problem . The mass of an electron is . × – kg. If its K.E.
is . × – J, calculate its wavelength. Since