Plank's Hypothesis

(i) A chamber containing black body radiations also contains simple harmonic oscillators of molecular dimensions which can vibrate with all possible frequencies.

(ii) The frequency of radiation emitted by an oscillator is the same as the frequency of its vibration.

(iii) An oscillator cannot emit energy in a continuous manner. It can emit energy in the multiples of a small unit called quantum (photon). If an oscillator is vibrating with a frequency v, it can only radiate in quantas of magnitude hv i.e., the oscillator can have only discrete energy values E_n given by
E_n = n h v
where n is an integer and h is Planck's constant (6.625 x 10^-34 joules-sec).

(iv) The oscillators can emit or absorb radiation energy in packets of hv. This implies that the exchange of energy between radiation and matter cannot take place continuously but are limited to discrete set of values 0, hv, 2hv, 3hv, nhv.


Planck's quantum hypothesis is considered as a radical departure from classical theory, because it considers that the energy of the oscillating particle of atomic dimension is taken as discrete rather than continuous and it helped to explain many physics phenomena of 20th century.

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According to de-Broglie's duality principle, a moving particle is associated with a wave which is known as de-Broglie wave. The wavelength of the matter wave is given by
lamda = h / (mv) = h / p
where m is the mass of the material particle, v its velocity and p is its momentum.

The arrangement of the experiment which led to its direct experimental verification is shown in figure. The apparatus consists of electron gun G where the electrons are produced and obtained in afine pencil of electron beam of known velocity. The electron gun consists of a tungsten filament F heated to dull red so that electrons are emitted due to thermionic emission. Now the electrons are accelerated in the electric field of known potential difference. After this the electrons are collimated by suitable slits to obtain a fine beam. The beam of electrons is directed to fall on a large single nickel crystal, known as target T. The electrons, acting like wave, are diffracted in different directions. The angular distribution is measured by an electron detector (Faraday cylinder C)

which is connected to a galvanometer. The Faraday cylinder can move on a circular graduated scale S between 200 to 900 to receive the reflected electrons. The Faraday cylinder consists of two walls which are insulated from each other. A retarding potential is maintained between them so that only fast moving electrons coming from electron gun may enter inside it. The secondary electrons (slow electrons) produced by collision with atoms from nickel target are reflected by Faraday cylinder. In this way the galvanometer

deflection is only due to electrons coming from electron gun. The Faraday cylinder was moved on the circular scale and for a given accelarating voltage V,

the scattering curve showed a peak in a particular direction theta. With the electron beam incident perpendicular to the crystal surface, the pronounced scattering direction was found to be 500 for electrons accelerated to 54 volts. Under these conditions, the surface row of atoms act like the ruling of a diffraction grating, producing the first order spectrum of 54 volts electrons at theta = 500. Since interatomic distance for nickel crystal is known to be 2.15 x 10-15 m, the interplaner distance d = 2.15 x 10-15 sin 250 = 0.09 x 10-10 m. Using Bragg formula 2 x 0.909 x 10-10 sin(900 - 250) = 1 lamda. Here angle theta is the angle between the incident beam and the interatomic plane. So, lamda = 1.65 x 10-10 m = 1.65 A0 According to de-Broglie electron wave lamda = 12.26 / (square root of 54) = 1.67 A0 As the two values are in good agreement, hence

confirms the de-Broglie's duality principle.

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