Compare and contrast the ideas that led to the Bohr model of

Compare and contrast the ideas that led to the Bohr model of the atom to the ideas that led to the quantum mecchanical theory that gave rise to the hydrogen atom wave functions.

Solution

The difficulty with the planetary picture provided before the Bohr model is that it is inconsistent with a well established fact of classical electrodynamics which says that an accelerated electric charge must continually radiate energy. If electrons actually followed such a trajectory, all atoms would act as source of radiation. The radiated energy would come from the kinetic energy of the orbiting electron; as this energy gets radiated away, As a result the electron would quickly fall into the nucleus. According to classical physics, no atom based on this model could exist for more than a brief fraction of a second.

In contrary The Bohr model is a mixture of classical physics and quantum physics. The main postulated of Bohr\'s orbit are as follows:

1.) The electron in the atom moves in a circular orbit centred on its nucleus. Its motion in the orbit is governed by the Coulomb electric force between the negatively charged electron and the positively charged proton.The radius of orbit can be given as [r = nh/(2*pi*m*v), where n is principal quantum number. Emission spectrum of hydrogen is nicely explained by Bohr model. However, one serious difficulty with the Bohr model was that it was unable to explain the spectrum of any atom more complicated than hydrogen.

2.) An electron in a Bohr orbit does not continuously radiate electromagnetic radiation. Its energy is therefore constant. The orbit is referred to as a stationary orbit.

3.) Electromagnetic radiation is only emitted when the electron changes from one orbit to another of a lower total energy. (The electron is said to undergo a transition.) In such a case, the energy lost, E, is emitted as one quantum of radiation of frequency f as given by the Planck–Einstein formula:

E = hf

Although the Bohr model hypothesis for the quantization of angular momentum can be justified in terms of electron wave ideas, the Bohr model remains profoundly unsatisfactory as a wave model for the atom and also was not able to answer that why it doesn\'t fall into the nucleus. The main failures of Bohr\'s model are:

- a mixture of classical and quantum ideas (electrons move classically on orbits, but their possible energy states are quantified)

- postulates that on the allowed orbits electrons do not radiate

(conflict with Maxwell’s theory)

- could not account for the maximal electron numbers on one shell

- could not explain splitting of the spectral lines in magnetic fields

- it is a non-relativistic theory although the speed of the electrons is close to c

In the Quantum Mechanical Model, the electron is treated mathematically as a wave. The electron has properties of both particles and waves. The advantage of Quantum Mechanical model over Bohr model is that it was successful to give explaination of the fact that electron does not fall inside nucleus.

The Bohr model was a one-dimensional model that used one quantum number to describe the distribution of electrons in the atom. The only information that was important was the size of the orbit, which was described by “n” the principle quantum number. Unlike Bohr\'s model, Quantum Mechanical Model allowed the electron to occupy three-dimensional space. It therefore required three coordinates, or three quantum numbers, to describe the distribution of electrons in the atom. Therefore nucleus is surrounded by electron cloud because of Heisenberg\'s uncertainty principle; one cannot measure the exact position of a particle. In this case, the electron cloud is a region where an electron can be probably found. Quantum Numbers used to give information about the location of an electron in an atom with respect to its energy level, sublevel, orbital, and spin. Every electron has a set of four quantum numbers. No two electrons have the same set of four quantum numbers. So hydrogen atom wave functions can be expressed in terms of all set of quantum numbers.