Bohr's Model (1913): Description, Differences, Limitation!!

HISTORY OF BOHR'S MODEL

In 1913, Bohr’s atomic model improved upon Rutherford’s earlier nuclear model. Rutherford’s 1911 model proposed that atoms have a dense, positively charged nucleus surrounded by electrons, but it couldn’t account for atomic stability or discrete spectral lines. Bohr addressed this by suggesting that electrons orbit the nucleus in fixed paths with specific energy levels. Electrons only release or absorb energy when moving between these paths, which explains atomic spectra, particularly for hydrogen. This concept of quantization was a significant advancement, connecting classical physics and quantum theory, although it was later supplanted by more precise quantum mechanical models.

BOHR'S POSTULATES (BOHR'S ATOMIC MODEL)

Bohr modified Rutherford’s model by applying Quantum theory to elucidate the structure of hydrogen atom. According to Bohr’s model:

An atom consists of a dense nucleus situated at the centre with the electron revolving around it. An electron cannot rotate about the nucleus in any chosen orbit but in certain selected orbits only whose angular momentum (mvr) is an integral multiple of h/2π i.e., mvr = h/2π where m = mass of the electron, v = velocity of the electron, n = 1, 2,3, ……. = Number of orbits in which electron is present and is known as the Principal Quantum Number, r = radius of the orbit and h = Plank’s constant.

When an electron rotates along any of the selected orbit, it does not radiate energy at all. These quantum selected orbits are called stationary orbits or stationery states, not that the electron is stationary but that no radiation occurs during rotation of electrons along these orbits.
If energy is supplied to an electron, it may jump from lower energy level to a higher energy level absorbing energy. Similarly, the excited electron jumps down to a lower energy level by emitting energy.

Thus, energy absorbed or, emitted if an electron, jumps can be represented by the following equation ΔE = E2 ~ E1 = hν. Where E1 and E2 are the energies of the electron in the first and second energy levels and ν is the frequency of radiation absorbed or emitted.

DIFFERENCES B/W RUTHERFORD'S AND BOHR'S MODEL

Bohr’s model developed on Rutherford’s by including quantised electron orbits, in which electrons move at fixed energy levels around the nucleus without emitting energy. Unlike Rutherford’s model, which failed to explain atomic stability, Bohr’s model accounted for discrete spectral lines by allowing electrons to move between various energy levels. For this reason, there are many differences between these two models.

RUTHERFORD'S MODEL	BOHR'S MODEL
1. Electrons can revolve around the nucleus in circular orbits of any radius.	1. There are several fixed and defined orbits for electrons to rotate.
2. As the electron orbits the nucleus in a circular path, its energy gradually decays and the atom becomes unstable.	2. No energy is lost when rotating in stable orbits of atoms with different energies i.e. the atom is permanent.
3. A continuous spectrum should be obtained from atoms, but in reality, discrete line spectra are obtained.	3. Discrete lines spectrum form the atoms.
4. The spectrum of the hydrogen atom cannot be explained.	4. The spectrum of the hydrogen atom can be explained.

BOHR'S QUANTUM THEORY OF HYDROGEN ATOM

Working on the above postulates, Bohr was able to calculate (I) the radii of various orbits in which electron of hydrogen like species (species having one electron such as H, He⁺, Li²⁺, Be³⁺ etc.) can reside and (II) Energy of the electron moving in different orbits around the nucleus in hydrogen like species having z = atomic number, m = mass, e = charge of an electron, h = Plank’s constant, n = Principle Quantum Number, E = energy of the quantum level.

Success of Bohr Model

Bohr’s model for the first time could explain the hydrogen spectrum as well as the spectrum of hydrogen like one electron species (He⁺, Li²⁺, Be³⁺ etc.).
This theory enables one to calculate the radius of the various stationery orbits with one electron system.
This theory for the first time introduced the idea of Quantum Numbers and the electronic transitions.

Limitation of Bohr's Theory

This theory cannot explain the spectrum of atoms or, ions containing two or, more electrons.
This theory failed to explain the splitting of some of the spectral lines into a group of finer lines under the influence of magnetic and electric field. The appearance of several lines implies that, there are several energy levels of nearly similar energy for each principal quantum number n. This necessitates the existence of new Quantum Numbers.
Bohr considered a two dimensional model of the atom, but actually an atom is three dimensional.
Bohr assumed that an electron in an atom is located at a definite distance from the nucleus and is revolving with a definite velocity around it. This is against Heisenberg’s Uncertainty Principle which states that it is impossible to determine simultaneously the exact position and momentum (velocity) of electron.

WAVE MECHANICAL CONCEPT OF THE ATOM: DE BROGLIE CONCEPT

In Bohr’s model, has assumed that an electron is a material particle revolving round the nucleus in circular orbits. But de Broglie in 1924 pointed out that the electron, like light, exhibit wave as well as particle nature, i.e., electron has a dual character. This concept of dual character of matter gave birth to the wave mechanical theory of matter, according to which the electrons, protons and even atoms when in motion, possess all wave properties.

de Broglie derived a relationship for the calculation of wavelength (λ) of the wave associated with a particle of mass m moving with velocity v as given below:

λ = h/mv or, λ = h/p

[p = mv = momentum of the particle]

h = Plank’s constant,

m = mass of the particle and

v = velocity of the particle.

If radius of circular orbit is r, circumference = 2πr.

So, if the electron-wavelength is λ,

2πr = nλ [n= 1, 2, 3, …….] ……….(1)

Here the figure shows 4 complete waves in a complete orbit, i.e. n = 4.

Again, according to de Broglie’s hypothesis, if the electron has mass m and velocity v,

λ = h/mv [h = Planck’s constant]

So, 2πr = nh/mv

or, mvr = nh/2π [n= 1, 2, 3, …….] ……..(2)

Obviously, the values of r and v will be different for different values of n; letting these values be r_n and v_n respectively for a fixed n,

mv_nr_n = nh/2π [n= 1, 2, 3, …….] …….(3)

This is Bohr’s quantum condition. So, it turns out, the quantum condition is consistent with de Broglie’s concept of matter-waves. However, it should be remembered that the above discussion is an oversimplification as an explanation of the allowed orbitals of atoms. Without the full application of quantum physics, its true explanation is not possible.

Although de Broglie equation is true for all particles in motion, i.e., whether small or, large, the concept of wave-particle duality is a real importance in the case of very small particles like electron and it is insignificant for the large particles, because in such case the de Broglie wave length is too small to measure.

HEISENBERG UNCERTAINTY PRINCIPLE

In quantum mechanics, the uncertainty principle is any of a variety of mathematical inequalities asserting a fundamental limit to the accuracy with which the values for certain pair of physical quantities of a particle. Such as position, x, and momentum p, can be presented from initial conditions.

Formula:

Δx = uncertainty in position,

Δp = uncertainty of momentum,

h = Plank’s constant, and π = pi

Example: Boron trifluoride hybridization.

CONCLUSION

Bohr’s model represented a major progress in comprehending atomic structure through the introduction of quantized electron orbits. It effectively clarified the stability of atoms and the emission spectra of hydrogen. Nevertheless, the model had constraints, especially in its failure to accommodate more intricate atoms and the wave-like nature of electrons, which was later addressed by quantum mechanics. Despite these deficiencies, Bohr’s model established the groundwork for modern atomic physics and stands as a crucial advancement in the development of atomic models.

Bohr’s Model (1913): Description, Differences, Limitation!!