Bohr’s Atomic Model

Dalton was the first chemist to introduce that atoms were the smallest form of matter in 1803. Several years later, Rutherford performed the famous experiment with a radioactive element, radium and a thin gold foil. 

Based on the concentration and deflections of the alpha rays, Rutherford concluded that there is a mass of positive charge at the centre of the atom, but surrounding the nucleus are negatively charged electrons. 

However, his hypothesis had two major flaws — instability of the entire atomic structure and lack of information on the hydrogen spectra. 

Then, Niels Bohr introduced the reality of the atomic structure in the famous Bohr Model formula in 1913. 

What Led to the Discovery of Bohr’s Model?

Rutherford’s gold foil experiment was a huge contribution because he was the first to explain the atomic structure, the positions of the nucleus and electrons in the atom and so on. 

However, his theory had two significant drawbacks, which completely contradicted the principle of mass.  

1. His model proposed that electrons were in continuous motion. 

It contradicted Maxwell’s theory that particles in continuous motion emit radiation and lose energy. It means that electrons continuously lose energy and follow a spiral path till they fall into the nucleus. Moreover, it implied that the atomic structure is not stable. 

If that had been the truth, then the existence of matter would be under question.

2. Another major drawback was his assumption about the continuous line spectra because electrons emit energy constantly. However, the spectra observed in the lab were discrete. 

As Rutherford’s model contradicted the very existence of matter, it was considered incomplete. That is what led to the conception of the Bohr Model formula. 

What is Bohr’s Model of the Atomic Spectra? 

It is essential to have a basic idea about the atomic spectra to learn everything about the Bohr Model of hydrogen atom. It is a pattern of the atoms’ energy that allows scientists and researchers to study elemental behaviour. 

There are two types of atomic spectra:

1. The emission spectrum represents the energy released by excited atoms when an element is heated. 

2. The line spectrum is the uniqueness of every element that describes the number of orbits, the energy differences and electronic behaviour. 

Bohr conceptualised his theory of the hydrogen spectrum based on these types. 

Bohr’s Atomic Theory 

In 1913, Niels Bohr introduced the theory about the hydrogen line spectrum and the reasons behind the discontinuities in the lines. His theory also proved the question of the stability of the atomic structure. That is why his theory is a major game-changer.  

Besides, the Bohr Model formula is defined based on the quantum theory of Planks that says: 

1. Every matter emits or absorbs a certain amount of energy in small packets known as quantum. 

2. For light energy, a quantum is known as a photon. 

3. The formula defines a photon’s energy: E= hf, where h is the Plank’s constant and f is the frequency. 

Rules of Bohr’s Atomic Model Theory 

The following postulates explain the Bohr Model of hydrogen atom: 

1. The centre contains the concentration of the entire atomic mass. The positively charged particles, called protons, are present here. The electrons surround the nucleus and constantly revolve in non-radiating energy orbits known as stationary orbits. 

2. These stationary orbits have fixed energy, so they are also known as energy levels. The greater the distance between the orbit and the nucleus, the more the energy will. Considering the orbital number system, K is the closest orbit and has the least energy while M, N and so on have a high amount of energy.

3. Bohr’s formula for energy levels also defines that one of those orbits is permissible, where the angular momentum of the electrons can be a whole multiple of h/2π. 

4. When electrons jump from one energy level, it emits or absorbs a certain amount of energy in the form of Quantums. Here, the amount of energy in the Qantas is equal to the gap between the energy of the E₁ and E₂ stationary orbits. 

Formulae of Bohr’s Postulates

We use the following formula to determine the relationship between the number of the orbit and electrons’ angular moment: 

mvr = NH/2𝜋

where m is the mass of an electron, v is the velocity, r is the radius of the orbit, h is Planck’s constant and n is the number of the orbit. 

For defining the energy emission or absorption of the electrons, the Bohr’s formula for energy levels: 

E1 – E2 = hf

Or, En = – (2𝜋2me4z2k2/n2h2)

Differences between Bohr’s Model and Rutherford’s Theory

Hydrogen Spectra Explanation based on Bohr’s Theory

The entire hydrogen spectrum comprises discontinuous lines with varied spaces. We can classify it  into five segments: Lyman, Balmer, Paschen, Brackett and Pfund. 

Bohr’s theory of hydrogen spectrum explains that the electron present in the atom jumps to higher energy levels on being excited. However, such a state is highly unstable and soon, the electron jumps back to the lower energy level, thereby losing energy. 

The amount of energy lost is different based on the energy level differences. Therefore, the line spectra are discontinuous and uneven. 

Conclusion 

The Bohr Model formula gave a new direction to the study of atomic structure. Niels Bohr used quantum theory to explain that electrons can only revolve in the permissible orbits based on the angular momentum and Planck’s constant. 

However, the lack of mathematical proof prevented the acceptance of his theory as a scientific law. Moreover, it was based on a single element. Therefore, it did not describe the behaviour of other atoms having more electronic states. 

That is why Schrodinger’s wave equations and Heisenberg’s Principle are said to prove mathematical expressions for the generalised behaviour of the electrons.