Saturday, January 31, 2015

De Broglie Hypothesis and Wave Nature of Particle

Particle nature of light

Photoelectric effect of light can be explained only when we assume that light these interacting with the matter like a particle. These wave packets are called quanta and they have fixed amount of energy. The energy particles are also called photons and they do not have the rest mass. It can be confirmed that when the light is interacting with the matter, it behaves like a particle.

With the increase of intensity, there will be more number of photons are available in the given light. These photons are electrically neutral and they are not deflected in electric and magnetic fields. When photon collides with a particle, its total energy and momentum are always conservative.

De Broglie Hypothesis

To explain the properties of the light like interference, diffraction and polarization, we shall depend on wave nature of the light. Simultaneously to explain the properties like photoelectric effect and Compton effect, light shall have particle nature.

As the same light is exhibiting both the set of properties, it shall also have dual nature.
In the universe the energy is broadly in the format of matter and radiation. There is a basic concept in the nature which tells that nature loves symmetry. We see so many things in the nature which are symmetrical.

We can explain the concept of symmetry easily. We know that the solar system is a macroscopic system where the sun is at the Center and the planets revolving around it. We also know that the item is a microscopic system where the nucleus is at the Center and the electrons are revolving around it. So we can see a broader symmetry in the design of the nature.
It is already proved that light is having dual nature. It travels like a wave and it interacts like a particle. We know that in the nature both light and the particles are forms of energy’s. As one form of energy is having dual nature and as nature loves symmetry, it is understood that the matter is also having dual nature.

It means to say that all the particles that we see are also having the wave nature. It means the electrons, the protons are not only having the behavior of the particles, and they can also behave like the waves under suitable conditions. This concept is called dual nature of matter. When the particles are travelling like waves they are called as matter waves.

As per the day Broglie’s concept the wavelength of the particle is equal to the ratio of Planck’s constant to the momentum of the particle. Experimentally it is proved that the particle can have wave nature.

So it can be concluded that electrons can behave like waves and can undergo diffraction. We can express the momentum in terms of kinetic energy as well as the applied potentiality as shown below.

We can also express the wavelength of the particle in terms of absolute temperature. It is based down the total energy particle can have for a particular temperature. This equation is derived basing on kinetic theory of gases.

In the above diagram we are also having a problem where the applied potential is given for an electron and we are supposed to calculate the corresponding wavelength of the electron. By converting the momentum into the kinetic energy and further in terms of the voltage with can solve the problem as shown above.

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