Bohrs Atomic Model and Its Limitations

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Introduction to the Bohr Atomic Model

A quantized shell model of an atom was given by Bohr in 1913 to provide an explanation of how electrons can stably orbit around the nucleus. This model provided a remedy for the stability problem under the previous Rutherford model of the atom, which displayed a motion where electrons would lose their energy and subsequently spiral into the nucleus due to the emission of electromagnetic radiation by the charged particles. Bohr's model was backed up by the classical law of physics and the quantum theory of radiation. 

Also, Niels Bohr atomic theory featured fixed size and energy of the electrons moving in orbits around the nucleus which is charged positively similar to the motion of planets around the sun. 

To describe Bohr's atomic model, it can be said that the energy levels of the electrons concentrate on the size of the orbits. Therefore, smaller orbits will have lower energy electrons. The reason for atoms being unstable is that electrons jump to lower orbits causing radiation. Now, an atom which is in the state of the smallest orbit will be completely stable as the electron will not have a lower orbit it can jump to. It was hence proposed that an electron can jump in-between these orbits by gaining or releasing photons (energy).


Features of the Niels Bohr Atomic Model

The following are the chief characteristics of the atomic model given by Niels Bohr.

  • Negatively charged electrons revolve around a positively charged nucleus in an atom. These electrons have definite circular paths known as orbits or shells.

  • Each of the circular paths has fixed levels of energy and are called orbital shells in terms of this atomic model.

  • The energy levels of electrons at different orbits are represented by n= 1, 2, 3…. (integers) and are known as quantum numbers. These numbers are assigned to the shells such as K, L, M, N for 1, 2, 3, 4 respectively. The lowest energy level of an electron is n=1 which is closest to the nucleus and is generally said to be the ground state. 

  • By gaining energy (or photons), an electron can jump to an orbital shell with higher energy, and by losing energy, it can jump to a lower energy level or orbital shell.


The Hydrogen Spectrum

The Neil Bohr atomic model is utilized to explain the working and structural formation of a hydrogen atom and it's energy levels. Each orbital shell indicates a quantum number 'n' associated with corresponding energy levels. 'eV' represents the unit amount of each energy level. The maximum energy level an orbital shell can have is the ionization energy of 13.598 eV.

Now, when electrons move between the different energy levels in a hydrogen atom, a spectrum is produced. This means that during the transition of electrons to different energy levels, the transmission of light appears. There are four different wavelengths present in a visible spectrum of light in a hydrogen atom. These refer to the excited state of electrons that transition down to a minimum of n=2 and are described by the Balmer equation.


Equations Included In The Bohr Model of Hydrogen Atom

  • The difference between the two energy levels (assuming E1, E2) and Planck's constant corresponds to the energy absorbed or emitted:

 ΔE = E2-E1 = hv

Where, 

  • ∆E is the energy that is emitted or absorbed

  • h is Planck's constant

  • v is the frequency of electromagnetic radiation 

  • The aforementioned formula leads to the derivation of Rydberg’s formula. This formula provides meaning to different energy transitions. The hydrogen atom emits several wavelengths of light which depends on the initial and final stages. The Rydberg formula is:

\[\overline{v}\] = \[\frac{1}{λ}\] = \[R(\frac{1}{n_1^2} - \frac{1}{n_2^2})\]

  • The momentum of an electron while revolving in shells is angular in nature. This is given by:

mevr = nh/2π

Where, 

  • n is the number of the energy shell

  • me is mass 

  • v is the velocity

  • r is the radius 

  • h is the Planck's constant


Limitations of Bohr’s Atomic Model

The following are the basic limitations of Bohr’s Model of the hydrogen atom.

  • It does not comply with the Heisenberg Uncertainty Principle. The Neils Bohr atomic model hypothesis considers electrons to have both known position and momentum simultaneously, which is unthinkable as indicated by Heisenberg. 

  • The Bohr atomic model did not make correct predictions of large-sized atoms and provided sufficient information only for smaller atoms.

  • It does not clarify the Zeeman impact when the spectrum is split into a few wavelengths within the sight of a magnetic field. 

  • It does not clarify the Stark impact when the spectrum gets separated into almost negligible lines within the sight of an electric field.

FAQ (Frequently Asked Questions)

1. How did Sommerfeld modify Bohr’s Model?

Answer: Sommerfeld introduced the new modification to Bohr’s atomic model in 1915. He gave the idea that electrons spin round the core in an elliptical path. Circular shells are shaped in unique conditions just when the major and minor axes of the orbit are equivalent. The core in the Bohr model holds the majority of the molecule's mass in its protons and neutrons. The electrons, which contribute little as far as mass, however, are electrically equal to the protons in the core, circle the positively charged nucleus.

2. What is meant by Planck’s constant?

Answer: Planck had presented his constant in 1900 clarifying the light radiation produced from heated bodies. Planck hypothesized that energy must be transmitted or ingested in discrete sums, which he called quanta. With Planck's speculation, notwithstanding, the radiation can happen just in quantum measures of energy. In case the brilliant energy isn’t exactly the quantum of energy, the measure of light in that recurrence reach will be decreased. Planck's equation effectively portrays radiation from heated bodies. Planck's constant has the elements of activity, which might be communicated as units of energy duplicated by time, units of force increased by length or units of angular momentum.