Applications of Bohr’s Model for JEE

In Atomic Physics, the Bohr model is one of the first things you learn because it improvised and changed many concepts in the right direction. This model was initially accepted as the rectification of the very famous Rutherford Model. Coined by Niels Bohr in the year 1913, the model took into account the structure and mechanism of the Solar system. The planets were replaced by the orbiting electrons, the Sun is analogous to a dense nucleus and the gravitational pull by electrostatic force.

The model proposed by Ernest Rutherford in 1911 had the following features regarding what an atomic model looks like.

1. It is also called the planetary model of the atom.

2. The atom has a concentrated mass which is tiny and positively charged called the nucleus with tiny negatively charged elementary particles called electrons revolving around it.

3. The dense nucleus explained the alpha-scattering experiment.

4. This model discarded the “plum-pudding” atomic model by Sir J.J. Thomson in which the electrons were embedded in the nucleus.

Let us further discuss the Bohr model and the main points it emphasises.

Important Points about Bohr Model

The Bohr Model was the first model in Atomic Physics that successfully introduced the concept of Quantum Mechanics concepts for explaining the atomic model. 

The main important points of this model are listed below:

1. The electrons that revolve around the nucleus do so in fixed paths known as circular orbits that have the same energy level and size. These orbits are named as K, L, M, and so on shells.

2. There is a direct relationship between the size of the orbit and the energy. The smallest orbit has the lowest energy.

3. Whenever there is a transfer or jump of an electron from one orbit to another, there is emission or absorption of electromagnetic radiation. If an electron jumps from a higher level to a lower level, the electron de-excites and emits radiation while when the electron goes from lower orbit to upper orbit there, the electron has to absorb radiation. 

The Hydrogen atom model is the simplest model to be explained by the Bohr model. The spectrum of the hydrogen atom was found to be discrete, like a line spectrum without being a continuous one. The Bohr model successfully explained the spectrum on quantum mechanical grounds. The energy levels having definite and discrete energies cause the electrons to either gain or lose that amount of energy for the jump from one orbit to another. This explains the discrete wavelengths emitted by them and the obtained line spectrum.

The Bohr model also introduces us to the principal quantum number n (a positive integer) and how the energy of an orbit is expressed through this quantum number. The orbits have a fixed radius and the energy is quantized in them. Mathematically, the radius of an orbit can be expressed as:

$r\left( n \right)={{n}^{2}}\times {r_1}$ 

Here, r1 is the radius of level n = 1, i.e., the smallest radius allowed for the case of the Hydrogen atom. This is also called Bohr’s radius. This is calculated to have the value of:

${r_1}=\text{0}\text{.529 }\!\!\times\!\!\text{ 1}{{\text{0}}^{\text{-10}\ }}\text{m}$ 

${r_1} =0.529\ \cdot{ \alpha }$

Bohr also calculated the energy expression of a given orbit,

$E(n)=\frac{-13.6\ eV}{{{n}^{2}}}$ 

Here, the value 13.6 eV is the value of the lowest energy orbit. So, we can see how they are interconnected with each other, i.e., the radius, the principal quantum number, and the energy. 

Applications of the Bohr Model

Now, let us move on to some important applications of the Bohr model. Even though the Bohr model is one of the simplest atomic models, it has many important applications.

A few remarkable applications of the Bohr model are as follows:

• The model has some significant impacts on setting up the grounds for quantum mechanics in explaining various observations. 

• The spectrum of hydrogen and hydrogen-like atoms were explained very accurately using this model. 

• Classical Physics had so much popularity that the quantum mechanical postulates were not getting the attention or importance they deserved. After the explanation, it was hard to avoid quantum mechanics altogether. 

Limitations of the Bohr Model

Despite being the most appreciated theory or model in atomic physics, Bohr’s model has some limitations too.

The limitations of the Bohr model are as given below:

1. The model explained the Hydrogen atom smoothly but it failed to explain complex atoms having atomic numbers much higher than the hydrogen atom.

2. It only explained the occurrence of the line spectrum but it couldn’t explain their intensity. Some lines were found to be more intense than the others without any explanation.

3. Upon closer inspection of the spectra, it was found that there was even more splitting into the lines obtained for any atom. There was no explanation for the fine structure splitting or hyperfine structure of the lines in the Bohr model.

4. There was a direct contradiction of Heisenberg’s uncertainty principle because Bohr’s model certainly claimed to predict the radius and velocity of an electron in a certain orbit using the value of n.

Summary

The conclusive points that can be drawn are listed below:

1. Bohr’s Theory explained the spectrum of hydrogen or hydrogen-like atoms successfully.

2. This theory introduced the idea of quantum mechanics in explaining physical phenomena.

3. The electrons revolve around a dense nucleus which is positively charged in some fixed paths or obits defined by principal quantum number n.

4. The radius of an orbit is expressed as $r\left( n \right)={{n}^{2}}\times r(1)$

5. The Bohr radius r1 has the value of $\text{0}\text{.529 }\!\!\times\!\!\text{ 1}{{\text{0}}^{\text{-10}\ }}\text{m}$.

6. The energy expression is given as $E(n)=\frac{-13.6\ eV}{{{n}^{2}}}$.