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# Chapter Three: Wave particle duality

الكلية كلية التربية للعلوم الصرفة     القسم قسم الفيزياء     المرحلة 3
أستاذ المادة فؤاد عطية مجيد       04/11/2018 17:51:56
3.1 De Broglie hypothesis
An important step in the development of a satisfactory quantum theory
occurred when Louis de Broglie in 1929 in his PhD work postulated that:
? Nature is strikingly symmetrical.
? Our universe is composed entirely of light and matter.
? If light has a dual wave-particle nature, perhaps matter also has this
nature.
The dual nature of light shows up in equations;
Each equation contains within its structure both a wave concept (?;? ), and a
particle (p; E).
The photon also has an energy given by the relationship from the relativity
theory
where p is the momentum of the photon.
This does not mean that light has mass, but because mass and energy can be
interconverted, it has an energy that is equivalent to some mass. De Broglie
postulated that a particle can have a wave character, and predicted that the
wavelength of a matter wave would also be given by the same equation that
held for light, where now p would be the momentum of the particle
Example: What is the de Broglie wavelength of an electron whose kinetic
energy is K = 100 eV?
Calculate the velocity of the electron from which we then find the de Broglie
wavelength corresponding to that velocity.

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