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The extent of localization of a particle...

The extent of localization of a particle is determined roughly by its de Broglie wave. If an electron is localized within the nucleus (of size about `10^(-14)`m) of an atom, what is its energy? Compare this energy with the typical binding energies (of the order of a few MeV) in a nucleus and hence argue why electrons cannot reside in a nucleus.

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To solve the problem, we need to determine the energy of an electron that is localized within the nucleus of an atom, which has a size of approximately \(10^{-14}\) m. We will use the de Broglie wavelength concept to find the energy and then compare it with typical binding energies in a nucleus. ### Step 1: Determine the de Broglie wavelength The de Broglie wavelength (\(\lambda\)) of a particle is given by the formula: \[ \lambda = \frac{h}{p} \] where \(h\) is Planck's constant and \(p\) is the momentum of the particle. For an electron localized within the nucleus, we can assume that the de Broglie wavelength is approximately equal to the size of the nucleus: ...
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