[Physics Class Notes] on Bohr Model of the Hydrogen Atom Pdf for Exam

In 1897, Sir J.J. Thomson discovered electrons as negatively charged particles present in every element’s atom, but without any knowledge of the distribution of electrons, the positive charge, and the mass inside the atom. Subsequently, in 1904, Sir Thomson suggested a model for the atom, also known as the ‘plum pudding model,’ which stated that the electrons are embedded like plums in a distribution (or pudding) of positive charge within the atom. Thomson’s model failed to explain emission spectra and alpha particle scattering. Rutherford came up with another model in which the electrons revolve around the nucleus in different orbits. The revolution is driven by the electrostatic force of attraction between the nucleus and the electrons. But Rutherford’s model failed to account for the stability of atoms and the origin of line spectra. To address the shortcomings of these previous models, Prof. Neils Bohr, in 1913, applied Planck’s quantum theory and proposed three postulates that came to be known as the Bohr Model of Atom. So, let us discuss the Bohr Model of Hydrogen Atom (class 12) in detail.

Prior to Bohr, there were a number of scientists who were working on the structure of an atom. Rutherford was one of them and his model was the closest one to the Bohr model of the atom. In fact, Niels Bohr had helped to overcome the problem in Rutherford’s model of an atom. 

Rutherford’s model of an atom had a major drawback, that it could not explain the stability. It showed that electrons in an atom revolve around a positively recharged centre called the nucleus. However, later on, it was found that any particle in a circular motion would undergo acceleration and thus would lose energy. So the electron would take a spiral path and would finally fall into the nucleus and the atom would collapse. But this is not true because this does not take place in reality. 

Bohr said that electrons do revolve around the nucleus but their energy remains fixed. He explained that the energy of the electrons remains fixed because they are restricted to some fixed orbits. Each of these orbits is at a fixed distance from the nucleus and is associated with a fixed amount of energy. These energy levels are represented by the letters K, L, M, N, or the numbers 1, 2, 3, 4, starting from the centre. 

So the final model of Neils Bohr was similar to Rutherford’s model of an atom which states that an atom consists of a positively charged centre in which the electrons revolve. The only difference was that in Bohr’s model, electrons revolve around the nucleus in fixed orbits with fixed energy. For his work on the structure of the atom, he got a Nobel Prize in 1922. 

Bohr’s Theory of Hydrogen Atom and Hydrogen-like Atoms

A hydrogen-like atom consists of a tiny positively-charged nucleus and an electron revolving around the nucleus in a stable circular orbit. 

Bohr’s Radius: 

If ‘e,’ ‘m,’ and ‘v’ be the charge, mass, and velocity of the electron respectively, ‘r’ be the radius of the orbit, and Z be the atomic number, the equation for the radii of the permitted orbits is given by r = n2 ｘr1, where ‘n’ is the principal quantum number, and r1 is the least allowed radius for a hydrogen atom, known as Bohr’s radius having a value of 0.53 Å. 

Limitations or Problems of the Bohr Model

• The theory Bohr devised was a mixture of classical and quantum physics. Quantum physics superseded classical physics, meaning quantum physics has everything classical physics has. This makes the approach of understanding the model of the atom invalid in some aspects. 

• The model could not explain the various intensities of the spectral lines, which are classified under the Stark effect. 

• The model could not explain the existence of the hyperfine structure of some spectral lines.

• The model makes inaccurate spectral line predictions when it is concerned with larger atoms such as helium, lithium and oxygen or any other element. Bohr’s model only works with hydrogen.

• The model does not explain the Zeeman effect, which is the splitting of spectral lines when placed in the magnetic field.