PARTICLE NATURE OF LIGHT: THE PHOTON

Photoelectric effect thus gave evidence to the strange fact that light in
interaction with matter behaved as if it was made of quanta or packets of
energy, each of energy hv.
Is the light quantum of energy to be associated with a particle? Einstein
arrived at the important result, that the light quantum can also be
associated with momentum (hv/c ). A definite value of energy as well as
momentum is a strong sign that the light quantum can be associated
with a particle. This particle was later named photon.

Wave Nature of Matter

The wave nature of matter is one of the most counter-intuitive concepts in Physics. You have seen examples of both particle nature of light and wave nature of light. You know about the Photoelectric effect due to Albert Einstein’s courtesy. In the photoelectric effect, the electrons and photons exhibit the properties of a particle, just like a billiard ball.

De Broglie’s Equation

Light and radiation are both particles and waves, according to De Broglie’s hypothesis, thus matter must also have a particle and wave character. Wave theory was born as a result of the de Broglie connection.

De Broglie’s equation is given as:

Λ = h ⁄ p = h ⁄ (mv)

Where,

Λ is the wavelength of particle,

P is the momentum of a particle,

H is the Planck’s constant,

M is the mass of particle, &

V is the velocity of the particle.

De Broglie’s Hypothesis

The momentum of a photon having energy E is given as:

P = E ⁄ c

The speed of light in a vacuum is represented by the letter c.≥

Planck’s idea states that the energy of a photon is determined by its frequency and wavelength.

E = h v = h c  ⁄ λ

The energy should be equal, implying:

H c  ⁄ λ = p c

Λ = h ⁄ p

De Broglie concluded that the aforementioned relationship should apply to particles as well. P=mv is the momentum of a particle with mass m moving at a speed of v. As a result, it must have a wavelength of

Λ = h ⁄ p = h ⁄ (mv)

DAVISSON AND GERMER EXPERIMENT
The experiment is performed by varying the accelerating voltage from 44 V to 68 V. A strong peak observed in the intensity (I) of the scattered electron for an accelerating voltage of 54 V at a scattering angle 50º. The appearance of the peak in a particular direction is due to the constructive interference of electrons scattered from different layers of the regularly spaced atoms of the crystals. From the electron diffraction theory, the wavelength of matter waves producing maxima at 50º is calculated to be λ= 0.165 nm. 

Thus, there is an excellent agreement between the theoretical value and the experimentally obtained value of de Broglie wavelength. Davisson- Germer experiment thus strikingly confirms the wave nature of electrons, particles in general and the de Broglie relation.

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