Is there any trick to find the group number and period number of a given element with large atomic number. Eg; 114,117,120 etc.

Dear student,
For finding the group number and period number of elements having large atomic number, You need to know the atomic numbers of Inert gases. For example, if we need to know group and period of atomic number 117, then we know that last inert gas of 7th period has atomic number as 118. Hence 117, would be just before it, and hence it will belong to halogen family having group number 17 and period 7. Atomic number 120 will be just two after 118, so definitely will belong to alkaline earth metals or group 2 of periodic table and period would be 8.

Hope it helps
Regards

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