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# Wave particle duality in micro maters physics

Wave particle duality

What is Wave particle duality ? This is the concept of quantum mechanics, which states that every particle or quantum entity may be partly described in terms not only of particles but also of wave.

The study of the behavior of light and other electromagnetic radiation, including the properties of wave like interference and radiation demonstrate the wave nature of light.

But photoelectric effect, Compton scattering, phenomenon point to the particle nature of light.

The properties of Light like interference and diffraction show the wave nature of light, while the emission and absorption show the particle behavior.  This phenomenon is called wave particle duality

More so gamma ray which behaves like electromagnetic wave of short wave length, through the detention of Geiger Muller tubes which count pulse, show that they behave as particles.  This can be called wave particle paradox, since wave and particle seem to be mutually exclusive.

The relationships in wave particle duality

E=hf

P=h/ 𝛌

Where E =energy of the particle , h= plank constant , f=frequency of the wave, p = momentum of the particle  and 𝛌 = wavelength , of the wave

From the two equation above, P and E, are talking about, mater as  particle while f and 𝛌 are talking about mater as a wave , and h the plank constant being the constant of proportionality in the both equations

So

E=hf

P=h/ 𝛌,

but  =c/f

so p=hf/c

P=E/c

E=pc=mc2   m

Therefore as particle the mass is given as

M=E/c2  = hf/c2

Wave particle duality

Wave nature of mater

Electron which can be classified as mater , because it has weight and occupy space, exhibits the properties of wave , like reflection, diffraction and interference

Germer in 1927, while studying the nature of crystal surface, directed beam of a electron to the surface of crystal, found out that electrons reflected in the same way x ray would have reflected from the same crystal.

From the Broglie equation 𝛌=h/mv, the calculated wavelengths were comparable to those obtained using x ray.

Apart from reflection as the evidence, of wave nature of mater, it was also confirmed, that mater at times behave like wave, by electron diffraction experiments.

In  electron diffraction experiments, a beam of electrons were passed through a crystal solid (very thin of graphite) the electrons diffracted from carbon atom and resulting circular pattern obtained on the screen is  a series of concentric  ring , due to regular spacing of carbon atom in different layers in the graphite.

Germer and davisson found out that electrons and molecules exhibit wave properties like diffraction and interference. But Broglie equation is universally validated and must expressed.

For electron λe =h/mv  ,  λ=1.2 x 10-10m, where v=6 x 106ms-1

The slit require for this diffraction should be as small as  10-10m

Limitation of mater exhibiting wave  particle duality

For classical particle such as ball of 0.15kg , moving with 30ms-1, cannot exhibit wave properties , like interference and diffraction , because the wave length can be small as λ=1.49 x 10-34m.  So no such classical or macro particles can exhibit wave properties

Wave particle duality

Particle nature of mater

In case you have forgotten , wave  particle duality,  means that mater can behave as particle and at times behave like wave.

We have discussed wave nature of mater, now we are going to discuss particle nature of mater, using phenomena like photoelectric effect and Compton scattering

Photoelectric effect

If light is shone on a suitable material, electrons are being emitted from the material.  This process of releasing electrons is called photoelectric effect

Example, when ultraviolent light falls on zinc electrons are emitted from the zinc atom.

Note that electrons are emitted in this way , provided that the wavelength  of radiation is below certain value, depending on the material.  Because using a wavelength that is too long, even if the intensity is very strong and the experiment may be ran for long as you  want but no electron will be emitted .

Though a weak radiation of short wavelength may cause electron emission immediately.

When a radiation of low intensity is directed to a material, few electron are emitted, but if the radiation of high intensity is directed to a material the electrons emitted increase per a second

Compton scattering

Compton scattering  , is also one of the evidence  of particle nature of mater.

What is Compton scattering?

It is the scattering of photon by charged particles, usually electrons. The scattering lead to the lost in energy of the photon scattered, and also increases in the wavelength of the photon. The part of the energy of the photon is used in recoiling of electron.

The Compton scattering was discovered by Arthur holly Compton, in 1923 at Washington university in St. Louis. It was further verified by his graduate student .Y.H. Woo, in the following year.  Compton earned 1927 Nobel prize in physics for t he discovery

The effect of Compton scattering is that it demonstrate that light light cannot be explained purely as a wave phenomenon.

From the evidences of  the properties of light and other electromagnetic radiation  above, like diffraction, interference , photoelectric effect and Compton scattering, it show that light and other electromagnetic radiation  can be described as wave and sometimes as a particle . And this is called wave particle duality 