**Wave Particle Duality**

https://www.slideshare.net/slideshow/embed_code/key/CRKb3v30H4U8rC**Wave particle duality **from **Alessio Bernardelli**

From the foregoing discussions, we seem to be in a dilemma as to the nature of matter. Some experiments e.g. electron diffraction indicate that matter behaves like a wave, but other phenomena such a s photoelectric and Compton effect experiments indicate that matter behaves like a stream of particles or photons.

These two theories seem to be incompatible but both have shown to have validity. Thus matter appears to have a dual nature. This is referred to as the wave particle duality or the wave particle paradox.

As in matter, so is it with light. Some observable phenomenon in the nature of light, such as reflection, refraction, diffraction, interference and polarization can be interpreted or explained by assuming that light (or matter) behaves like waves. But other observable phenomena such as emission and absorption of light, photoelectricity, radiation of energy from heated bodies, thermionic emission can only be understood by assuming the particle nature of matter.

This dual nature of matter is known as the wave-particle duality or the wave particle paradox.

The wave particle duality refers to the idea that light and matter 9such as electrons) have both wave and particle properties, that is, light behaves either as a wave or as a particle but not as both simultaneously.

**The Uncertainty Principle**

In general, the process of making a measurement tends to alter the quantity being measured. This is very much pronounced in very small scales such as the atomic and the nuclear scales. As was first pointed out by Heisenberg, It is impossible in principle to make precise measurement of both the position (*x*) and momentum (*p*) of a particle simultaneously. In fact the more precisely the location of the particle *has* to be specified, the more uncertainty is introduced into the determination of its momentum and conversely too. Any such measurements have inbuilt uncertainties ∆*x *in the position and ∆*p* in the momentum. Such measurements can only be expressed as probabilities. Heisenberg showed that:

∆*x* . ∆*p ≥ h*

*∆x . ∆v ≥ h*

*∆E . ∆t ≥ h*

here ∆E, ∆t, ∆p and ∆x are the uncertainties in the energy, time, momentum and position measurements.

- Momentum and position,
- Energy and time,
- Position and velocity, are known as complementary variables.

Heisenberg Uncertainty Principle states that it is impossible to know accurately the exact position and momentum of a particle simultaneously. The uncertainty in the momentum multiplied by the uncertainty in the position approximately equals the Planck’s constant, *h*.

Because of the extremely small value of h (=6.63×10^{-34} Js) the uncertainty principle is of no consequence for objects above atomic sizes.

**Question**

A photon with a wavelength of 6.00 x 10^{-12} m collides with an electron. After the collision the photon’s wavelength is found to have been changed by exactly one Compton wavelength (2.43 x 10^{-12} m).

- What is the photon’s wavelength after the collision?
- 3.57 x 10
^{-12}m B. 8.43 x 10^{-12}m C. 6.00 x 10^{-12}D. It could be either one of the above