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jaumzaum
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I cannot understand why the electron orbit should be an integer multiple of De Broglie wavelength. Why should the wave path "fit" the electron orbit for it to be stationary?
If I correctly understood his concepts, the electron has wave nature, and for a stable situation it should be in phase with itself around the nucleus. See also :jaumzaum said:I cannot understand why the electron orbit should be an integer multiple of De Broglie wavelength. Why should the wave path "fit" the electron orbit for it to be stationary?
The electron orbit is an integer multiple of De Broglie wavelength because of the wave-particle duality of electrons. According to De Broglie's theory, all particles have a wave-like nature, and the wavelength of this wave is inversely proportional to the momentum of the particle. In the case of electrons, their momentum is quantized, meaning it can only take on certain discrete values. This leads to their De Broglie wavelength also being quantized, and the electron orbit being an integer multiple of this wavelength.
The De Broglie wavelength of an electron is related to its orbit through the Bohr model of the atom. In this model, the electron's orbit is determined by its angular momentum, which is quantized in units of h/2π. This angular momentum is also related to the electron's momentum, which, as mentioned before, is inversely proportional to its De Broglie wavelength. Therefore, the quantized values of the electron's momentum and angular momentum result in its orbit being an integer multiple of its De Broglie wavelength.
The fact that the electron orbit is an integer multiple of De Broglie wavelength is significant because it provides evidence for the wave-like nature of electrons. This concept was crucial in the development of quantum mechanics, which revolutionized our understanding of the behavior of subatomic particles. It also has practical applications, such as in the design of electron microscopes, where the wavelength of electrons is used to produce high-resolution images.
No, the electron orbit can only be an integer multiple of De Broglie wavelength. This is because the quantization of the electron's momentum and angular momentum is a fundamental property of particles, and cannot be changed. Therefore, the electron's orbit will always be an integer multiple of its De Broglie wavelength.
Changes in the De Broglie wavelength of an electron can affect its orbit in a few ways. Firstly, a larger De Broglie wavelength would correspond to a lower momentum, which would result in a larger orbit. On the other hand, a smaller De Broglie wavelength would lead to a higher momentum and a smaller orbit. Additionally, the De Broglie wavelength is also related to the energy of the electron, so changes in the wavelength can also affect the energy levels of the atom and, consequently, the electron's orbit.