Question

What is the atomic number of lanthanum whithout aufba principle

Answer 1

There are a number of series that rule how the electrons are configured in the orbitals.

The Aufbau principle (theoretical model):
1s<2s<2p<3s<3p<4s<3d<4p<5s<4d<5p<6s<4f<5d<…..

The Rydberg rule (from experimental/spectroscopic data):

1s<<2s<2p<<3s<3p<<3d<4s<4p<<4d<5s<5p<<4f<5d<6d…

 The Aufbau principle, the one that you are referring to as the rule for filling orbitals is taught as a scientific law in high-school but in reality there are a lot of exceptions on this rule. Even in high-school you might have come up to the exceptions of period 3 - the first row that includes transition metals- namely Cr (4s1 3d5) and Cu (4s1 3d10) where the 3d orbital is filled - or half-filled- prior to the 4s orbital. The logically inconsistent idea here is that in a transition metal atom, 4s is occupied before 3d but 4s is also easier to ionise. We tell students that the (n+1)s is of lower energy, thus more stable and for that reason is filled first and then we start making excuses to explain why the ns can loose one electron to the (n+1)d orbital later due to the increased stability that a full or half-full nd orbital provides which is not exactly correct.

Here is some missing background: 
1)A distinction between Kohn-Sham density functional orbitals, the ones fulfilling a simple Aufbau rule and describing the lowest experimental configuration for energy averages and the canonical Fock orbitals, describing experimental vertical ionisations and obeying a more complex Aufbau rule known for high spin/low spin complexes is necessary.

2)The order of orbital filling cannot be derived directly from orbital ionisation energies, neither experimentally nor theoretically because there is no general simple relation owning to possible orbital reorganisations. A given kind of nd and (n+1)s energies can vary from d(x-2)s(2) to d(x-1)s(1) to d(x).

So we expect electrons to configure accordingly to the lowest energy Kohn-Sham orbitals, but there is always the case of them occupying the corresponding canonical Fock orbitals that are not necessarily the lowest in energy. This depends on spin-spin interactions and chemical environments that are also in effect.