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Dalton was the first chemist to introduce the fact that matter is made from small elements called atoms, which was considered the smallest form of matter at that time. 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, he 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 theory proved two major flaws- instability of the entire atomic structure and lack of information on the hydrogen spectra. Niels Bohr introduced the reality between the atomic structure in the famous Bohr Model formula.
What led to the discovery of Bohr’s Model?
Rutherford’s gold foil experiment was a huge contribution because he was the first to give an idea about the atomic structure, the positions of the protons and electrons in the atom, and so on. However, his theory had two major drawbacks, which completely contradicted the principle of mass.
He said that electrons continuously lose energy and follow a spiral path till it falls into the nucleus. If that had been the truth, then the existence of matter would be under question. Moreover, it implied that the atomic structure is not stable.
Another major drawback was his theory about the continuous hydrogen spectra because electrons emit energy constantly. However, when the spectrum was observed in the lab, it was line spectra.
As Rutherford’s model contradicted the very existence matter, it was considered incomplete. This is what led to the conception of the Bohr Model formula.
What is Bohr’s model of the hydrogen atom?
Hydrogen atomic spectra
It is important to have a basic idea about the atomic spectra to learn everything about the Bohr Model of hydrogen. It is a pattern of the atoms’ energy that allows scientists and researchers to study elemental behaviour. There are two types of atomic spectra:
The emission spectrum represents the energy released by excited atoms when an element is heated.
The line spectrum is the uniqueness of every element that describes the number of orbits, the energy differences, and electronic behaviour.
On this basis Bohr’s theory of the hydrogen spectrum was conceptualised.
Introduction to 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 that the question of instability of the atomic structure as per Rutherford’s model was invalid. This is the main reason why his theory is considered as the major game-changer. Besides, the Bohr Model formula is defined based on the quantum theory of Planks that says:
Every matter emits or absorbs a certain amount of energy in small packets known as quantum.
For light energy, a quantum is known as a photon.
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 Bohr Model of hydrogen can be explained by his postulates which are as follows:
The entire atomic mass is concentrated at the centre, where the positively charged particles, called protons, are present. The electrons surround the nucleus and constantly revolve in non-radiating energy orbits known as stationary orbits.
These stationary orbits have fixed energy, so they are also known as energy levels. The greater the distance between the orbit and the nucleus, more will be the energy. 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.
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.
When electrons jump from one energy level, it emits or absorbs a certain amount of energy in the form of Qantas. Here, the amount of energy in the Qantas is equal to the gap between the energy of the E₁ and E₂ stationary orbits.
Formulas of Bohr’s postulates
To determine the relationship between the number of the orbit and electrons’ angular moment, the following Bohr model formula is used:
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 is made from discontinuous lines with varied spaces and classified into five segments- Lyman, Balmer, Paschen, Brackett, and Pfund. In Bohr’s theory of hydrogen spectrum, it has been explained 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. As the amount of energy lost is different based on the energy level differences, the line spectra are discontinuous and uneven.
Conclusion
The Bohr Model formula has definitely given 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, his theory didn’t have any mathematical proof, which is why it wasn’t accepted as a law. Moreover, it was based on a single element, and therefore, the behaviour of other atoms having more electronic states wasn’t described properly. That’s why Schrodinger’s wave equations and Heisenberg’s Principle are said to prove mathematical expressions for the generalised behaviour of the electrons.
