Prinsiya na Dukkanin Hada a Cikin Karamin Daɗi

A cikin haka na farko da Photoelectric effect, Crompton’s effect da Bohr’s model of atom, ana sani da abubuwa da ya gane da kuma tufafi mai sauƙi da suka faruwa a kan juna ko kuma tufafi masu sauyi Quanta.
Amma, Huygen’s Principle da kuma abubuwan da aka samun daga Young’s double slit experiments sun bayar da wani abu mai zurfi da ya shafi da cewa juna yana cikin alama ko ba suka faruwa.

Abubuwan da aka samun daga double slits sun bayar da wani abu mai zurfi da ya shafi da cewa juna yana cikin alama. Wannan ta haɗa da lalacewar da ya faru a kan nau'in juna. A shekarar 1704, Newton ya sanya da nau'in suka faruwa a kan juna saboda corpuscular theory.

Babu daga cikin labar da zaɓe te ke da zama da kyau don bayyana duk abubuwan da suka faruwa a kan juna. Saboda haka, ilimin sama sun hada da shiga da cewa juna yana da nau'in alama da kuma nau'in suka faruwa. A shekarar 1924, mutanen ilimi na Faransa, Louis de Broglie ya kawo takardun batu. Ya sanya cewa duk baya a duniya yana da nau'in alama, idan ya yi, duk baya a duniya, idan ya ce photon ko elephant, yana da alama mai girma da shi, ita ce an sami ko ba an sami ba. Ya kafa wavelength zuwa duk baya da mass m da kuma momentum p kamar yadda ake amfani da

Idan, h shine Planck constant da p = mv, v shine velocity of the body.

Saboda mass mai yawa da elephant, ya fiya da momentum mai yawa, kuma ya fiya da wavelength mai tsawo, wanda ba a iya samun ba. Amma, baya masu tsawo kamar electrons, suna da mass mai tsawo, kuma suna da wavelength mai girma da ya fi samun. Tabbacin de Broglie ya taimakawa don bayyana orbit masu sauti a kan Bohr’s model of atom. Electron zai zama a kan orbit idan length ta shi ya fi koyar da integral multiple da natural wavelength ta shi, idan ba a iya koyar da wavelength ta shi, wannan orbit ba zama ba.

Tashoshin da Davisson da Germer suka yi a kan electron diffraction from a crystal da kuma interference pattern similar da ya samun a kan bombarding a double slit with electrons sun haɗa da tabbacin matter wave theory ko kuma wave particle duality theory.

Compton Effect

A cikin photoelectric effect, juna yake fitowa a kan metal a kan beam of particles called photons. Energy of one photon contributes to the work function energy of one electron as well as provides the kinetic energy to that emitted electron. These photons are the particle like behavior of light wave. Sir Albert Einstein proposed that light is the collective effect of huge number of energy packets called photon where each photon contains energy of hf. Where h is the Planck constant and f is the frequency of the light. This is a particle like behavior of light wave. The particle like behavior of light-wave or other electromagnetic wave can be explained by Compton effect.

A cikin wannan binadar, x-ray beam of frequency fo da kuma wavelength λo yake fitowa a kan electron. Ba a yi fitowa da x-ray, electron da x-ray yake fitowa su ne a kan axis of incident x-ray. Wannan fitowa ta haɗa da principle of energy conservation kamar fitowar Newtonian’s particles. An samun cewa ba a yi fitowa, electron yake yanayi a kan direction mai yawa da x-ray yake yanayi a kan direction na biyu, kuma an samun cewa diffracted ray yana da frequency da wavelength da ba suka faruwa ba. Saboda energy of the photon varies with frequency, an samun cewa incident x-ray yake ci gaba da energy during collisions, da kuma frequency of the diffracted ray yana da ci gaba da that of the incident x-ray. Ci gaban energy of x-ray photon contributes to the kinetic energy for the movement of the electron. Wannan fitowa da x-ray ko photon da electron yana da kayan fitowa da Newtonian’s particles such as Billboard balls.

Energy of photon is given by

Therefore the momentum of the photon can be proved as

Which can be written as,

From equation (1) it can be concluded that a electromagnetic wave with wavelength λ will have the photon with momentum p.
From equation (2) it can be concluded that a particle with momentum p is associated with wavelength λ. That means wave has particle like characteristics, the particle on movement also exhibits wave like behaviour.

As we already said, this conclusion was first drawn by De Broglie and hence this is known as De Broglie hypothesis. As the wavelength of the moving particle is expressed as

Where, p is the momentum, h is Planck constant and wavelength λ is referred as De Broglie’s wavelength. De Broglie explained that as the electrons orbit around the nucleus it will also have the wave like behaviour along with its particle like characteristics.

Divission and Germer Experiment

The wave nature of electron can be proved and established in many different ways but most popular experiment is Divission and Germer in the year of 1927. In this experiment they used a beam of accelerated electrons which normally strikes on the surface of a nickel block. They observed the pattern of scattered electrons after striking on the nickel block. They used an electron density monitor for this purpose. Although it was expected that the electron should be scattered after collision in different angle with respect to the axis of the incident electron beam but in the actual experiment it was found that the density of scattered electrons was more at particular angles than other. This angular distribution of the scattered electrons is very similar to an interference that of light diffraction. Hence this experiment clearly shows the existence of wave particle duality of electrons. The same principle can be applied to the proton and neutrons too.

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