Question

Write the postulates of Bohr’s theory of atoms.

Answer 1

Hint: The Bohr theory of the atom was explained using the structure of the hydrogen atom. He presented four postulates for this model, each explaining the orbit of an electron, energy of an electron, energy absorbed/emitted during electronic transitions and the angular momentum of an electron respectively.

Formulas used: $\nu = \dfrac{{\Delta E}}{h} = \dfrac{{{E_2} - {E_1}}}{h}$
Where $\nu $ is the frequency of radiation, $h$ is the Planck’s constant, ${E_1}$ and ${E_2}$ are the energies of the lower and higher allowed energy states respectively.

Complete step by step answer:
Bohr used the structure of the hydrogen atom to explain what he thought could be the structure of all atoms.
His first postulate described what an orbit of an electron is. It is as follows:

1) The electron in the hydrogen atom can move around the nucleus in a circular path of fixed radius and energy. These paths are called orbits, stationary states or allowed energy states. These orbits are arranged concentrically around the nucleus.
In the next postulate, he mentions about the energy of the electron in its respective orbit, and about transitions between different orbits:

2) The energy of an electron in the orbit does not change with time. However, the electron can move from a lower stationary state to a higher stationary state if a required amount of energy is absorbed by the electron or energy can be emitted when the electron moves from higher stationary state to lower stationary state. This energy change does not take place in a continuous manner.
The third postulate is one of the most important, as it gives us the relation between frequency of emitted/absorbed radiations during transition and talks about the energy difference between two orbits:

3) The frequency of radiation absorbed or emitted when transition occurs between two stationary states that differ in energy by $\Delta E$, is given by:
$\nu = \dfrac{{\Delta E}}{h} = \dfrac{{{E_2} - {E_1}}}{h}$
Where $\nu $ is the frequency of radiation, $\Delta E$ is the energy change, $h$ is the Planck’s constant, ${E_1}$ and ${E_2}$ are the energies of the lower and higher allowed energy states respectively.
The last postulate quantifies the angular momentum of an electron. That is, he gave a mathematical expression for the momentum of an electron in each orbit:

4) An electron can move only in those orbits for which its angular momentum is an integral multiple of $\dfrac{h}{{2\pi }}$, and that is why only certain fixed orbits are allowed. Expressed as an equation, we get:
${m_e}vr = n\dfrac{h}{{2\pi }}$ where $n = 1,2,3....$
${m_e}$ is the mass of an electron, $v$ is the velocity of the electron, $r$ is the radius of the orbit and $h$ is the Planck’s constant.

Note: Although the Bohr model of the atom could explain the stability and line spectra of the hydrogen atom and other hydrogen like species (ions having only one electron), it was unable to explain the spectrum of other elements. Also, it failed to explain the splitting of spectral lines in the presence of magnetic fields, known as the Zeeman effect, or in the presence of an electric field, known as the Stark effect. It also couldn’t explain the ability of atoms to form chemical bonds. Thus, the quantum model of the atom was proposed many years later.