DE BROGLIE’S EXPLANATION OF BOHR’S SECOND POSTULATE OF QUANTISATION

According to Bohr’s atomic model, angular momentum of electron is integral multiple of \fn_cm \large \frac{h}{2\pi}

\fn_cm \large i.e\;\;\left [ mvr=\frac{nh}{2\pi} \right ]

But what is the reason, Bohr himself could not give answer to it.

Finally after 10 years De Broglie found the reason. According to this, a particle of mass m moving with speed V is associated with a wave of wavelength λ is given by.\fn_cm \large \left [ \lambda=\frac{h}{mv} \right ]

According to De Broglie, orbiting electron around the nucleus of an atom is associated with a standing wave.

i.e only those DeBroglie waves exist for which the circumference of the circular orbit contains a  whole number of wavelength.

\fn_cm \large i.e\;\; 2\pi r=n\lambda

\fn_cm \large 2\pi r=n\left ( \frac{h}{mv} \right )

\fn_cm \large \left [ mvr=\frac{nh}{2\pi} \right ]

LIMITATION OF BOHR’S MODEL

  1. This theory is applicable only to simplest atom like Hydrogen (Z=1). This theory fails in case of atom for which (Z>1)
  2. This theory does not explain why orbits of electron are taken as circular while elliptical orbits are also possible.
  3. Bohr’s theory does not take into account of the wave properties of electrons.
  4. This model is unable to explain the relative intensities of the frequencies in the spectrum.

LASER LIGHT

The LASER stands for Light Amplification of Simulated Emission of radiation, developed in 1960.

Light is emitted from a source in the form of packets of waves. Light coming out from an ordinary source contain a mixture of many wavelengths. There is also no phase relation between the various waves. Therefore such light, even if it is passed through an aperture, spreads very fast and the beam size increases rapidly with distance.

In the case of Laser light, the wavelength of each packet is almost the same. Also the average length of the packet of waves is much larger. This means that there is better phase correlation over a longer duration of time. This results in reducing the divergence of a Laser beam substantially.

If there are N atoms in a source, each emitting light with intensity I, then

intensity produced by an ordinary source \propto NI

and Intensity produced by a laser source \propto N^{2}I

i.e light from a laser can be much stronger than that from an ordinary source.

It has entered into all areas of science and technology. There are low power laser, with a power of 0.5 mw, called pencil laser. There are also lasers of different power suitable for delicate surgery of eye or glands in the stomach. Finally there are laser which can cut or weld steel.

IMPORTANT LINKS OF WAVE OPTICS
Introduction  Alpha Particle Scattering and Rutherford’s Nuclear Model of Atom
Atomic Spectra Bohr Model of the Hydrogen Atom
The Line Spectra of the Hydrogen Atom De Broglie’s Explanation of Bohr’s Second Postulate of Quantisation
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