Bohrs Model

Introduction

The Bohr atomic model was proposed in 1913 by a Danish physicist named Neil Bohr. He improved on Rutherford's model of an atom. Rutherford explained that in an atom, the nucleus is positively charged and surrounded by electrons (negatively charged particles).

Bohr amended Rutherford's concept stating that electrons travel around in fixed orbital shells. He also stated that each orbital shell has a set of energy levels. As a result, Rutherford essentially defined an atom's nucleus, whereas Bohr advanced the model. He talked about electrons and the many energy levels that they have.

Postulates of Bohrs Atomic Model

• Electrons in an atom rotate around the nucleus in fixed concentric circular shells termed energy shells or energy levels, which are labelled as K, L, M, and so on.

• Each energy level is connected with a certain amount of energy E which increases as the distance from the nucleus increases, i.e. $\mathrm{E_1 \:\lt \:E_2\: \lt\:E_3}$ .

• An electron cannot absorb or emit energy as long as it is in a specific orbit. As a result, these orbits are sometimes known as stationary states or ground states.

• When an electron jumps from one energy level to another, it either emits or absorbs energy. This energy corresponds to the difference in energy between the two levels. It can be represented as

$$\mathrm{\Delta E\:=\:E_2\:−\:E_1\:=\:hv}$$

Where, $
u$ = frequency of energy absorbed/emitted

This indicates that an electron's energy cannot vary continuously but rather changes abruptly by a definite quantity, i.e. the energy of an electron is quantized.

• An electron's angular momentum in a given orbit is quantised, i.e. an electron's angular momentum can only have definite or discrete values as $\mathrm{m
  u r =n\frac{h}{2\pi}}$

Where, n = number of energy shell, 1, 2, 3, ….

m = mass of the electron

h = Plank's Constant

v = velocity of the electron

r = radius of the electron

Application of Bohrs Theory

Bohr's hypothesis could be applied to hydrogen atom which bear just one electron. The theory of Bohr could also be applied to hydrogen-like atoms which are single electron system. Only one electron exists in $\mathrm{Li^{2+}, He^+}$

Merits of Bohrs Model of Atom

• The observed values of radii and energy in a hydrogen atom are in agreement with those estimated using Bohr's theory.

• The emission and absorption spectra of hydrogen-like atoms are explained by Bohr's idea of the stationary state of electron.

• The observed values of the hydrogen spectrum's spectral lines are quite identical to those estimated by Bohr's theory.

Limitation of Bohr's Model of Atom

• The origin of the spectra produced by multielectron species cannot be explained by Bohr's hypothesis.

• The fine spectrum of hydrogen atoms cannot be explained by Bohr's hypothesis.

• In a magnetic field, an excited atom with a line emission spectrum has its spectral lines divided into a number of closely spaced lines. The Zeeman effect is the name for this occurrence.In the presence of an electric field, similar spectral line splitting is observed. The Stark Effect is the name for this occurrence. The effects are not explained by Bohr's model.

• In Bohr's hypothesis, the electron is a minuscule material particle that moves around the nucleus. However, according to De Broglie, the electron had dual nature.

• Bohr's model breaches Heisenberg's principle of uncertainty.

Conclusion

A significant number of lines are present in the hydrogen atom's emission spectrum. Based on his postulates, Bohr proposed an explanation. A significant number of atoms constitute any particular sample of hydrogen. Varying atoms absorb different quantities of energy when energy is provided to this sample of gas. Depending on the quantity of energy received by the atoms, the single electron present in different hydrogen atoms changes shift to various energy levels. Higher energy electrons become unstable and fall back to lower energy levels, producing energy in the form of a line spectrum with numerous lines of different frequencies and wavelengths.

FAQs

Q1. Can the energy of an electron be quantized as per Bohr’s Atomic Model?

Ans: Yes, Bohr stated that the energy of electron cannot change continuously. In fact, it changes by a definite amount using the formula

$$\mathrm{\Delta E\:=\:E_2\:−\:E_1\:=\:hv}$$

Where, $
u$ = frequency of energy absorbed/emitted

Q2. How does Bohr’s Atomic Model violate Heisenberg’s Uncertainty Principle?

Heisenberg stated that Bohr’s Atomic Model could not hold true since it is impossible to measure position and momentum simultaneously for an electron. Bohr's Atomic Model accounts to have both known radius and orbit for an electron.

Q3. State the advantages of Bohr's Atomic Model over Rutherford’s Atomic Model.

Ans: Bohr’s Atomic Model could explain the stability and line spectra for hydrogen atom and hydrogen atom like systems such as $\mathrm{He^+, Li^{2+}, Be^{3+}}$ whereas Rutherford could not configure the energy levels of the orbits.

Q3. What are the criticism faced by Bohr’s Atomic Model?

Ans: Bohr's Model could quantize the energy of electrons however it could not explain the following:

• Bohr's Model violated Heisenberg’s Uncertainty Principle.

• It could not explain Zeeman and Stark effect i.e. the effect of magnetic field and electric field on the spectral line splitting.

• Bohr's Atomic Model is valid only for one electron systems and not for multielectron systems.

Q4. How did Sommerfeld modified Bohr’s Atomic Model?

Ans: Sommerfeld quantized the orientation and shapes of the atomic orbitals to account for the additional energy levels in the fine spectral lines. As per Sommerfeld-Bohr’s Theory, the electrons revolve in elliptical orbits rather than circular orbits. However, the Sommerfeld- Bohr's Theory had its share of paradoxes.

Q5. Which nature of electron has been highlighted in Bohr’s Atomic Model?

Ans: de Broglie, a student of Bohr, hypothesized that the electrons have dual nature. The electrons could act as a wave or as a particle. Bohr’s Atomic Model accounted electrons as particles that are energy quantized.