Name: Bohr Atom Model: Frequency of Emitted Radiation
Uploaded: 2019-07-19
Duration: 3 min 54 s
Description: Electrons jump in different energy levels. Let's understand how we can calculate the frequency of emitted and absorbed radiation as electrons transition into...

Question

State Bohr&rsquo;s postulate to define stable orbits in hydrogen atom. How does de Broglie&rsquo;s hypothesis explain the stability of these orbits ?

Accepted Answer

Bohr's postulate to define stable orbits in hydrogen atoms states that an electron can revolve only in those circular orbits in which its angular momentum is an integral multiple of $n h / 2 π$ , where $h$ is Planck’s constant and $n$ is the principal quantum number of orbit. Thus, an electron can revolve only in certain orbits of definite radii. These are called stable orbits. An atom has a number of stable orbits in which an electron can reside without the emission of radiant energy. Each orbit corresponds, to a certain energy level.

De Broglie hypothesis explanation of the stability of orbits:
According to de Broglie, an electron orbiting around the nucleus is associated with a stationary wave. Electron wave is a circular standing wave. Since destructive interference will occur if a standing wave does not close upon itself, only those de Broglie waves exist for which the circumference of the circular orbit contains a whole number of wavelengths i.e., the circumference of $n^{t h}$ stable orbit for an electron can contain exactly $n$ wavelength of de-Broglie.

$\Rightarrow n λ = 2 {πr}_{n}$

$n (\frac{h}{p}) = 2 {πr}_{n}$

$n (\frac{h}{m v}) = 2 {πr}_{n}$

$m v r_{n} = \frac{n h}{2 π}$

$\Rightarrow L = \frac{n h}{2 π}$

This was the quantum condition proposed by Bohr.

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