Question

Describe the atomic model of Rutherford. How did Bohr model removed its drawbacks?

Hint:

For the Bohr model, remember that its genius was in defying classical physics with a few simple (but revolutionary) quantum rules to explain experimental facts.

Answer 1

Rutherford's Atomic Model (Nuclear Model):
Based on his famous alpha-particle scattering experiment, Ernest Rutherford proposed a model of the atom in 1911. Its main features are: \begin{enumerate} \item Nucleus: Almost all the mass and the entire positive charge of an atom are concentrated in a very small, dense region at the center called the nucleus. \item Empty Space: Most of the atom is empty space. \item Electrons: The negatively charged electrons revolve around the nucleus in circular paths called orbits, much like planets orbiting the sun. The electrostatic force of attraction between the nucleus and electrons provides the necessary centripetal force for their revolution. \end{enumerate} Drawbacks of Rutherford's Model: Rutherford's model was inconsistent with classical physics and experimental observations in two key ways: \begin{enumerate} \item Instability of the Atom: According to classical electromagnetic theory, an accelerating charged particle must radiate energy. An electron revolving in an orbit is constantly accelerating (due to the change in the direction of its velocity). Therefore, it should continuously lose energy and spiral into the nucleus, making the atom unstable. This contradicts the observed stability of atoms. \item Inability to Explain Line Spectra: As the electron spirals inwards, its frequency of revolution would increase continuously. This means it should emit a continuous spectrum of radiation. However, atoms (like hydrogen) are observed to emit a discrete line spectrum. \end{enumerate} How Bohr's Model Removed the Drawbacks: Niels Bohr, in 1913, modified Rutherford's model by introducing quantum concepts through three postulates: \begin{enumerate} \item Postulate of Stationary Orbits: Bohr proposed that electrons can revolve only in certain specific, non-radiating orbits called stationary orbits. While in these orbits, electrons do not emit energy. This postulate directly contradicted classical theory and solved the problem of atomic instability. \item Postulate of Quantization of Angular Momentum: The allowed stationary orbits are those for which the angular momentum of the electron is an integral multiple of \(h/2\pi\), where \(h\) is Planck's constant. (\(L = n \frac{h}{2\pi}\), where n=1, 2, 3...). \item Postulate of Frequency Condition: An atom emits radiation (a photon) only when an electron jumps from a higher energy stationary orbit (\(E_2\)) to a lower energy one (\(E_1\)). The frequency (\(\nu\)) of the emitted photon is given by \(h\nu = E_2 - E_1\). Since only specific orbits and energy levels are allowed, only specific frequencies of light can be emitted, thus explaining the observed discrete line spectra. \end{enumerate}