Atom, as a whole, is electrically neutral and therefore contains equal amount of positive and negative charges.
In Thomson’s model, an atom is a spherical cloud of positive charges with electrons embedded in it.
In Rutherford’s model, most of the mass of the atom and all its positive charge are concentrated in a tiny nucleus (typically one by ten thousand the size of an atom), and the electrons revolve around it.
Rutherford nuclear model has two main difficulties in explaining the structure of atom: (a) It predicts that atoms are unstable because the accelerated electrons revolving around the nucleus must spiral into the nucleus. This contradicts the stability of matter. (b) It cannot explain the characteristic line spectra of atoms of different elements.
Atoms of most of the elements are stable and emit characteristic spectrum. The spectrum consists of a set of isolated parallel lines termed as line spectrum. It provides useful information about the atomic structure.
To explain the line spectra emitted by atoms, as well as the stability of atoms, Niel’s Bohr proposed a model for hydrogenic (single electron) atoms. He introduced three postulates and laid the foundations of quantum mechanics: (a) In a hydrogen atom, an electron revolves in certain stable orbits (called stationary orbits) without the emission of radiant energy. (b) The stationary orbits are those for which the angular momentum is some integral multiple of \(h / 2 \pi\). (Bohr’s quantisation condition.) That is \(L=n h / 2 \pi\), where \(n\) is an integer called the principal quantum number. (c) The third postulate states that an electron might make a transition from one of its specified non-radiating orbits to another of lower energy. When it does so, a photon is emitted having energy equal to the energy difference between the initial and final states. The frequency \((v)\) of the emitted photon is then given by \(h \nu=E_i-E_f\) An atom absorbs radiation of the same frequency the atom emits, in which case the electron is transferred to an orbit with a higher value of \(n\). \( E_i+h \nu=E_f \)
As a result of the quantisation condition of angular momentum, the electron orbits the nucleus at only specific radii. For a hydrogen atom, it is given by \( r_n=\left(\frac{n^2}{m}\right)\left(\frac{h}{2 \pi}\right)^2 \frac{4 \pi \varepsilon_0}{e^2} \) The total energy is also quantised: \( \begin{aligned} E_n & =-\frac{m e^4}{8 n^2 \varepsilon_0^2 h^2} \\ & =-13.6 \mathrm{eV} / n^2 \end{aligned} \) The \(n=1\) state is called ground state. In hydrogen atom the ground state energy is -13.6 eV. Higher values of \(n\) correspond to excited states ( \(n>1\) ). Atoms are excited to these higher states by collisions with other atoms or electrons or by absorption of a photon of right frequency.
de Brogle’s hypothesis that electrons have a wavelength \(\lambda=h / m v\) gave an explanation for Bohr’s quantised orbits by bringing in the wave particle duality. The orbits correspond to circular standing waves in which the circumference of the orbit equals a whole number of wavelengths.
Bohr’s model is applicable only to hydrogenic (single electron) atoms. It cannot be extended to even two electron atoms such as helium. This model is also unable to explain for the relative intensities of the frequencies emitted even by hydrogenic atoms.
POINTS TO PONDER
Both the Thomson’s as well as the Rutherford’s models constitute an unstable system. Thomson’s model is unstable electrostatically, while Rutherford’s model is unstable because of electromagnetic radiation of orbiting electrons.
What made Bohr quantise angular momentum (second postulate) and not some other quantity? Note, \(h\) has dimensions of angular momentum, and for circular orbits, angular momentum is a very relevant quantity. The second postulate is then so natural!
The orbital picture in Bohr’s model of the hydrogen atom was inconsistent with the uncertainty principle. It was replaced by modern quantum mechanics in which Bohr’s orbits are regions where the electron may be found with large probability.
Unlike the situation in the solar system, where planet-planet gravitational forces are very small as compared to the gravitational force of the sun on each planet (because the mass of the sun is so much greater than the mass of any of the planets), the electron-electron electric force interaction is comparable in magnitude to the electron nucleus electrical force, because the charges and distances are of the same order of magnitude. This is the reason why the Bohr’s model with its planet-like electron is not applicable to many electron atoms.
Bohr laid the foundation of the quantum theory by postulating specific orbits in which electrons do not radiate. Bohr’s model includes only one quantum number \(n\). The new theory called quantum mechanics supports Bohr’s postulate. However in quantum mechanics (more generally accepted), a given energy level may not correspond to just one quantum state. For example, a state is characterised by four quantum numbers ( \(n, l, m\), and \(s\) ), but for a pure Coulomb potential (as in hydrogen atom) the energy depends only on \(n\).
In Bohr model, contrary to ordinary classical expectation, the frequency of revolution of an electron in its orbit is not connected to the frequency of the spectral line. The later is the difference between two orbital energies divided by \(h\). For transitions between large quantum numbers ( \(n\) to \(n\) – \(1, n\) very large), however, the two coincide as expected.
Bohr’s semiclassical model based on some aspects of classical physics and some aspects of modern physics also does not provide a true picture of the simplest hydrogenic atoms. The true picture is quantum mechanical affair which differs from Bohr model in a number of fundamental ways. But then if the Bohr model is not strictly correct, why do we bother about it? The reasons which make Bohr’s model still useful are: (i) The model is based on just three postulates but accounts for almost all the general features of the hydrogen spectrum. (ii) The model incorporates many of the concepts we have learnt in classical physics. (iii) The model demonstrates how a theoretical physicist occasionally must quite literally ignore certain problems of approach in hopes of being able to make some predictions. If the predictions of the theory or model agree with experiment, a theoretician then must somehow hope to explain away or rationalise the problems that were ignored along the way.