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.

Explanation

The de Broglie wavelength of electron,
`lamda=size of atom=10^(-14)m`
Corresponding to this wavelength, the electron possesses energy,
`E=(6.62xx10^(-34)xx3xx10^(8))/(10^(-14))=1.986xx10^(-11)J`
`=(1.986xx10^(-11))/(1.6xx10^(-13))=124.1MeV`
If the electrons possess energy of order of 124 Mev. They will not be able to stay inside the nucleous. it is bacause Coulomb's forca cannot provide such high value of binding energy to the electrons. Hence, electrons cannot reside inside the nucleus.