Question

Derive moseley law on the basis of Bohr's theory

Answer 1

First, consider an atom consisting of one electron orbiting a nucleus with atomic number ZZ. Since this is a hydrogenic atom, the energy levels of this electron are equal to

E=Z2Rn2E=Z2Rn2

for n=1,2,3,...n=1,2,3,..., where RR is the Rydberg energy. If the electron goes from level nn to level mm, it will emit a photon of energy

Ephoton=ΔEelectron=Z2R(1n2−1m2).Ephoton=ΔEelectron=Z2R(1n2−1m2).

Hopefully you can see that this equation is very similar to the one you have above. But why is ZZ replaced with (Z−σ)(Z−σ) in your equation? This is where the shell model comes in. The idea is that the other electrons in filled lower shells (which are negatively charged) partially screen the charge of the nucleus. In other words, to the outer electrons, it "looks like" there's a nucleus with a charge (Z−σ)e(Z−σ)e at the center, rather than the "bare" nuclear charge +Ze+Ze. We can therefore justify replacing ZZ with (Z−σ)(Z−σ) in the above expression.

This isn't a rigorous proof by any standard, of course, but hopefully it shows the connection to the shell model

hope this helps plzz mark this as brainliest.......