Bohr atomic model of Hydrogen | Bohr theory

At first, scientist Rutherford gave the atomic theory of atoms after the alpha particle scattering experiment. But this theory was unable to consistent with the stability of an atom. This theory of Rutherford was based on classical mechanics. To explain the stability of atoms, scientist Niels Bohr gave a theory or model which is known as the Bohr atomic model. He explained this theory for hydrogen like atoms by using quantum theory of scientist Max Planck. In this article, we are going to discuss the Bohr atomic model or Bohr theory for hydrogen atom. This will be helpful for the students of class 9 and class 12.

Contents in this article:

• Postulates of Bohr atomic theory
• Bohr atomic model of hydrogen
• Applications of Bohr atomic theory
• Drawbacks of Bohr atomic model

Postulates of Bohr’s atomic theory

To explain the stability of atoms, Bohr gave some postulates or assumptions before giving the atomic theory. These postulates are as followings –

1. Electrons inside an atom revolve around the nucleus in some allowed orbits.
2. During their revolution, electrons do not absorb or radiate energy. However, they can jump to a higher orbit after absorbing energy or can jump to a lower orbit after releasing energy.
3. The angular momentum of the electron is an integral multiple of \small \frac{h}{2\pi } and the corresponding allowed orbits are known as stationary orbits or stable orbits.

These are the three basic assumptions of Bohr’s atomic theory.

Bohr atomic model of hydrogen

Bohr atomic model can explain hydrogen atom and hydrogen-like atoms properly. All of the above postulates are applicable to hydrogen atom and hydrogen-like atoms. Bohr atomic theory is based on quantum mechanics. In spite of inconsistent with some classical experiments, Bohr model is accepted as the basis of atomic structure of all elements. This is because this model can successfully analyze the atomic spectrum of hydrogen atom. Again, this model is consistent with de Broglie theory of wave-particle duality.

From Bohr’s atomic model of hydrogen atom we became to know that

1. Radius of first Bohr orbit or K-shell of hydrogen atom is 0.529 angstrom or 0.0529 nanometer. The expression for the radius of n-th state of hydrogen atom is \small r_{n}=0.529n^{2} angstrom.
2. Ground state energy of hydrogen atom is -13.6 eV. For the n-th state the expression for energy is \small E_{n}=-\frac{13.6}{n^{2}} eV.
3. There are six types of series of hydrogen spectrum depending upon the final orbit of electron after a transition. These are Lyman series, Balmer series, Paschen series, Bracket series, Pfund series and Hamfrish series.

Series	Initial state	Final state	Equation for wavenumber
Lyman	n>1	n=1	\small \frac{1}{\lambda }=R[\frac{1}{1^{2}}-\frac{1}{n^{2}}]
Balmer	n>2	n=2	\small \frac{1}{\lambda }=R[\frac{1}{2^{2}}-\frac{1}{n^{2}}]
Paschen	n>3	n=3	\small \frac{1}{\lambda }=R[\frac{1}{3^{2}}-\frac{1}{n^{2}}]
Bracket	n>4	n=4	\small \frac{1}{\lambda }=R[\frac{1}{4^{2}}-\frac{1}{n^{2}}]
Pfund	n>5	n=5	\small \frac{1}{\lambda }=R[\frac{1}{5^{2}}-\frac{1}{n^{2}}]
Hamfrish	n>6	n=6	\small \frac{1}{\lambda }=R[\frac{1}{6^{2}}-\frac{1}{n^{2}}]

Here, the inverse of the wavelength lambda is known as the wavenumber and R is the Rydberg’s constant.

Applications of Bohr’s atomic theory

1. Using Bohr atomic model one can find the expressions for the radius of orbit and the speed and energy of the electron in any allowed orbit.
2. Spectrum of hydrogen atom and hydrogen-like atoms can be explained almost accurately by using Bohr’s atomic theory.
3. This theory helps to explain the main characteristics of atomic spectrum of alkali metals like Na, K, etc.
4. Bohr atomic model can establish the stability of atoms. This is why Bohr’s theory is more acceptable than Rutherford theory.

Drawbacks of Bohr atomic model

Although, Bohr atomic model can explain the stability of atom, spectrum of hydrogen atom and hydrogen-like atoms, it has some drawbacks. The limitations of Bohr’s atomic theory are as followings –

1. Bohr theory of atom cannot explain the atomic spectrum for the atoms other than hydrogen or hydrogen-like atoms.
2. Classical theory says that an accelerated charged particle emits electromagnetic radiation. So, accelerated electrons will also emit EM radiation which is not considered in Bohr’s atomic model. Again, Bohr’s theory of atom fails to explain why no electromagnetic radiation is emitted from the electron while revolving around nucleus under the centripetal acceleration.

These are two main failures of Bohr’s atomic model.

This is all from this article on Bohr atomic model of hydrogen atom. If you have any doubt on this topic you can ask me in the comment section below.

Thank you!

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