Q1. Why cerium(58) electronic configuration is written as 4f1 5d1 6s2 instead of 4f2 5d0 6s2 and why after cesium i.e. praseodymium(59) is written as 4f3 5d0 6s2, if they had started filling 5d first?

The discrepancies in the electronic configuration of these two elements are due to the fact that the 5d and 4f sublevels have very similar energies. The electrons can move easily from one to the other. The 4f sublevel becomes prominent as the lower-energy sublevel after it has a few electrons like in the case of Praseodymium.
 

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