i dont want a solution i want to learn a tutorial
and the solve it my self

" a free electron in rest caught by nucleus of Li+++ which its charge is +3e,
and then it goes to base condition.calculate the angular momentum of electron and the length
of a wave of the emitted photon"

 

A neutral Li atom has three electrons in it. Each of those electrons is described by a set of quantum numbers. Those quantum numbers are related to solutions of the Schroedinger Wave Eauation. So the energy and momentum of each electron in a neutral atom are quantized. What this means is that they are constrained to certain specific values. The Pauli Exclusion Principle (named after Wolgang Pauli) says that no two identical fermions can have the same set of quantum numbers.

http://en.wikipedia.org/wiki/Pauli_exclusion_principle

Moving to the case of our Li+++ Ion capturing electrons the first one should probably be assigned to the state with the lowest principal quantum number. It is called by Chemists the 1s level, where 1 is the principal quantum number and s is the name of the orbital that defines the angular momentum and thus the shape. The next electron captured by the Li++ Ion wil also go int the 1s orbital but with the opposite spin quantum number. This completes the 1s shell. The last electron that can be captured will go into the 2s shell and that's the end of the capture game.

So the 1s and the 2s are all you need to compute the change in energy which gives the wavelength of the emitted photon and the 1s, 2s will give you the angular momentum.

__________________
We never have time to do it right; but we always have time to do it over.

 

For hydrogen-like systems (one-electron systems) the energy goes as Z^2. Thus the ground state of this ion will have a ground state energy of 9 times the ground-state energy of the hydrogen atom.

For the wave length of the photon use E = hc/λ.