Dual Nature of Matter and Radiation

Dual Nature of Matter and Radiation PDF Notes, Important Questions and Synopsis

SYNOPSIS

An electromagnetic wave has dual (wave–particle) nature.

The wave nature of light can be observed in the phenomena of interference, diffraction and polarisation.
While photoelectric effect and Compton effect involve energy and momentum transfer, radiation behaves as if it is made of a bunch of particles-photons show particle nature of a wave.

Wave nature of matter

De Broglie said that wave nature was symmetrical and that the two basic physical entities—matter and energy-must have symmetrical character. If radiation shows dual aspects, so should matter.
De Broglie proposed that wavelength λ is associated with a particle of momentum p.
This wavelength is so small that it is beyond any measurement. This is the reason why macroscopic objects in daily life do not show wave-like properties.
De Broglie hypothesis
Matter shows dual character like electromagnetic radiation does. It also shows wave-like properties.
Apart from being a particle, a wavelength associated with matter is called de Broglie
wavelength. It is given by the relation,_{$begin mathsize 12px style straight lambda equals straight h over straight p end style$}
where m is the mass of the particle, v is speed and h is Planck’s constant.
On the left-hand side of the above equation, λ is the attribute of a wave, while on the right-hand side, the momentum p is a typical attribute of a particle.

De Broglie wavelength for a photon
De Broglie’s idea that matter also exhibits duality and has wave properties can be expressed quantitatively by first considering electromagnetic radiation.
A photon of frequency v and wavelength λ has energy:_{$begin mathsize 12px style straight E equals hv equals hc over straight lambda end style$}
De Broglie wavelength for an electron
If an electron (charge = e) is accelerated by potential difference of volts, then it acquires kinetic energy of
K=eV
Therefore, the formula can be written as
$begin mathsize 12px style straight lambda equals straight h over mn equals straight h over straight p equals fraction numerator straight h over denominator square root of 2 Km end root end fraction equals fraction numerator straight h over denominator square root of 2 eVm end root end fraction end style$

Substituting the numerical values of h, m and e,
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Davison and Germer experiment

Davisson–Germer electron diffraction arrangement

Result

It was noticed that a strong peak appeared in the intensity (I) of the scattered electron for an accelerating voltage of 54 V at a scattering angle θ = 50°.
This is due to the constructive interference of electrons scattered from different layers of the regularly spaced atoms of the crystals.
From the electron diffraction measurements, the wavelength of matter waves was found to be 0.165 nm.
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Photoelectric effect

When light falls on a metal surface, some electrons near the surface absorb enough energy from the incident radiation to overcome the attraction of the positive ions in the material of the surface.
After gaining sufficient energy from the incident light, the electrons escape from the surface of the metal into the surrounding space.
The photoelectric emission is an instantaneous process without any apparent time lag (〖~10〗^(-9)s or less) even when the incident radiation is made exceedingly dim.

Photoelectric effect

When light of an appropriate frequency (or correspondingly of an appropriate wavelength) is incident on a metallic surface, electrons are liberated from the surface. These photo- or light-generated electrons are called photoelectrons.
The incident light photon should be greater than or equal to the work function of the metal.
E ≥ W
hν ≥ W
ν ≥ W/h

Work function

The minimum energy required by an electron to escape from the metal surface is called the work function of the metal. It is generally denoted by W and measured in electron volt (eV).

Threshold frequency

The minimum frequency W/h required for emission of electrons is called threshold frequency. It is denoted by ν0.
ν0 = W/h (threshold frequency)

Effect of intensity of light on photocurrent

Photocurrent increases linearly with the intensity of incident light when accelerating potential is fixed.

Effect of potential on photoelectric current

The photoelectric current increases with an increase in accelerating (positive) potential.
The maximum value of the photoelectric current is called saturation current.
At saturation current, all the photoelectrons emitted by the emitter plate reach the collector plate.

Intensity of incident radiation

The photocurrent is found to decrease rapidly until it drops to zero at a certain critical value of the negative potential V0, which is called the retarding potential V0.
The minimum negative (retarding) potential given to the plate for which the photocurrent stops or becomes zero is called the cut-off or stopping potential.
Photoelectric current is zero when the stopping potential is sufficient to repel even the most energetic photoelectrons with the maximum kinetic energy (Kmax).
K max = e V0

Einstein’s photoelectric equation

The electron is emitted with maximum kinetic energy given by K max = hν – φ0.
Kmax depends linearly on ν and is independent of the intensity of radiation.
Photoelectric emission is possible only if h ν > φ0.
Greater the work function φ0, higher the minimum or threshold frequency ν0 needed to emit photoelectrons.
Photoelectric equation can be written as eV0 = h ν – φ0, for ν ≥ ν0.

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