the extent of localisation of a particle is determined roughly by its de broglie wavelength.if an electron is localized within the nucleus (of size of about 10^-14m) of an atom, what is its energy?In the solution of this question wavelength is taken to be10^-14m. but i can't understand how size of nucleus is equal to wavelength?
Here we are trying to prove that electrons cannot reside within the nucleus.. We can start by first considering that the wavelength (or reach of an electron or its physical limits) is of the order of the extent or diameter of the nucleus, this is done in order to suppose that an electron resides inside the nucleus.
Now, we have the associated energy of the electron as
E = hν
and it comes out to be
E = 124 MeV
which is very large compared to the binding energy of the nucleus, So, as the energy of electron in higher than the binding energy of the nucleus we can conclude that no electron can reside within a nucleus as it will not be able to hold a far more energetic electron (like it does protons and neutrons).