Question

What are the properties of matter waves ?

Answer 1

Hint: The de Broglie theory which states that light can have dual nature is governed by a set of properties which the matter waves are said to exhibit and hence the application of the concept of de-Broglie waves is required. The criteria under which the waves are said to be called de-Broglie waves need to be determined in order to state or list out the properties of matter waves.

Complete answer:
Light is capable of exhibiting a dual nature which means that it can obey both light and wave properties but not at the same time. According to de-Broglie a moving material particle is said to exhibit the wave nature at certain times and the particle nature at other times. The particle theory of light states that light travels through packets of energy also given by the corpuscular theory of light.

When a moving particle is said to exhibit particle nature the wave was named after the person who stated this theory. Hence these waves were called matter waves or de-Broglie waves. The de-Broglie equation for wavelength was given by the following equation:
$\lambda = \dfrac{h}{p}$
Here, $p$ is the momentum of the particle and $h$ is the Plank’s constant.

Knowing this let us state the properties of these matter waves: The de-Broglie theory is only applicable for moving particles or particles in constant motion.The theory used the concept of matter waves to find the probability of the location of a particle in space. This was done by using the square of the wave’s amplitude known given by concept of probability density in order to find out the whether the intensity of the matter wave is large or not

The basic principle behind these matter waves is that they describe the relationship between the wave nature and the particle nature by relating the wave characteristic, that is, wavelength with the particle characteristic, that is, momentum and hence this is given by the de-Broglie wavelength. All matter at a subatomic level, that is, at a microscopic level is said to obey the wave nature and hence the wave-like motion of particles like electrons and protons can be significantly observed.

The matter waves are named so because they are independent of charges because as per the equation given by de-Broglie the motion of the particle is dependent only on its wavelength, mass, velocity and hence its momentum.The matter waves are not electromagnetic in nature because electromagnetic waves are only associated with accelerated charged particles but the matter waves need not have charge in its material.

Since particles like electrons which are at microscopic level exhibit wave-like motion, they are said to have a de-Broglie wavelength only at certain conditions. Only those circular orbits made by particles like electrons round the nucleus are said to be stable whose circumference is an integral multiple of de-Broglie wavelength associated with it.

Note: Macroscopic objects do not show wave properties because as per the de-Broglie equation since the mass of these objects are large their wavelengths will be small since both of these quantities are inversely proportional. Hence, the wave-like motion will not be observed and they are not significant.