Dual Nature of Radiation and Matter – Important Topics

The matter is characterized by properties such as velocity, size, mass, etc., whereas waves are characterized by properties such as wavelength, wave velocity, etc. The term wave-particle duality or the idea of the dual nature of radiation and matter refers to the manner in which a particle behaves like a wave or vice versa under certain conditions. Nature loves coherence and uniformity. If light can exhibit wave-particle duality, it should also be exhibited by matter. Einstein’s exposition of the photoelectric effect resulted in de Broglie coming up with wave-particle duality; after this, a new horizon opened on the dual nature of radiation and matter. 

Emission of electron

All metals have free electrons, but they can’t escape from the metal surface because of ionic force. However, if free electrons are provided with proper energy, they would escape (emit) the metal surface. The minimum energy required for this emission is called the metal’s work function(ϕ0). It is different for different metals; e.g., Na has a work function of 2.75 eV, while Pt has 5.65 eV.

This energy (>ϕ0) can be provided to the metal surface by suitable heating (Thermionic emission), giving a strong electric field (Field emission) or appropriate frequency of light (Photoelectric emission). 

Photoelectric effect

It comes from the dual nature of radiation and matter. Electrons are emitted from a metal surface when illuminated with a suitable frequency of light; this phenomenon is named the photoelectric effect. The emitted electrons are called photoelectrons, and the minimum frequency of light below which this emission can’t take place is called threshold frequency. It differs from metal to metal. For example, Zn, Cd, Mg have a threshold frequency in the ultraviolet range, while Alkali metals (Li, Na, K are sensitive to the visible spectrum)

Photoelectricity is affected by

1. The intensity of light:

Photoelectric current increases linearly with the rise of the intensity of light.

       2.  Collector plate potential:

If the collector plate(A) is at a positive potential than the emitter plate(C) and the potential is increased, photocurrent would increase and after some time it would reach its maximum limit,  called saturation current. On the other hand, if we change the current polarity, photocurrent would decrease significantly and eventually, it stops. Therefore, the minimum negative potential applied to collector plate(A) for photocurrent to be zero(0) is called stopping potential.

Particle nature of radiation: Photons

The wave nature of electromagnetic radiation cannot explain the phenomenon of electron emission. In 1905 Einstein proposed that radiation (or light) is not just a wave, but it is the flow of particles with quantized energy. These particles are called photons. According to the proposal of Einstein, each quantum of a light wave of frequency f, a photon, carries the energy of

E = hf

where h = Planck Constant = 6.62607004 × 10-34 J . s

Einstein furthermore proposed that if electrons gain this energy of photons, and it exceeds its work function (ϕ0), then it would emit from the metal surface with the maximum kinetic energy of 

Kmax = hf – ϕ0; here, f is greater than the threshold frequency of that metal.

This is the equation known as Einstein’s Photoelectric equation. 

According to Sir Einstein, this absorption of light energy occurs at the atomic level. When the light is absorbed by the atom, the energy of the photon is transferred to it. If an object has many atoms, the energy transfer still occurs as a quantized amount of single-photon.

Wave nature of matter: Matter-wave

Nature loves symmetry. If the wave has a particle nature, particles (matter) may have wave nature, too, right? In 1924, Physicist Louis De Broglie made a similar proposal. If radiation has a particle nature, then a beam of moving particles can have a wave nature. This wave is called the Matter Wave. According to Louis De Broglie, the wavelength of matter-wave,

λ = hp

λ is called De Broglie wavelength,

h is Planck constant

p is the momentum of a particle

From this, we can see (mathematically) wave nature (wavelength λ) and particle nature (momentum p) in a single equation. 

In 1927, C.J.Davisson and L.H. Germer experimentally verified De Broglie’s proposal. Electrons are subatomic particles, but a beam of electrons showed an interference pattern in the experiment. Similar patterns can be seen with neutrons, protons, and other atoms. 

But why can we not see a moving bus or taxi showing wave nature?

We know, p=mv

p = momentum of particle/object

m = mass of particle/object

v= velocity of particle/object

from the De Broglie equation, we can write

λ = hmv

We can see that for larger objects (bus, taxi or any other macro-objects), the mass in the denominator of the right-hand side of the equation is so large that the resulting wavelength( λ ) becomes very small. So, in reality, we can not see the wave nature of these objects.

Example of dual nature of radiation and matter – 

• Photoelectric cells

Photoelectric cells are nothing but a collector plate (Anode) and a semi-cylindrical emitter plate (Cathode) in a vacuum tube connected with a cell. It transfers light energy into electrical energy. It has various applications, from generating sound in films to photo-telegraphy.

• Scanning Tunneling Microscope (STM)

An optical microscope works under visible light or ultraviolet light(f=300 nm), so we cannot see smaller dimensions <300 nm. STM comes to our aid here by using electron tunneling through potential barriers.

Conclusion

Scientists have multiple observations about the dual nature of matter and radiations. For example, C.H.Davisson and L.H.Germer conveyed that electrons behave like waves with a wavelength that acknowledged the formula De Broglie proposed. The Einstein equation and the De Broglie equations prove the dual nature of radiation and matter.