The atomic number at which filling of the g-orbital is likely to begin is :

121

The correct answer is option 1. 121.

Filling of \(d\)-orbitals starts after filling of \(s\) and \(p\) orbitals for a specific shell. We see this pattern repeating in the periodic table.

Similarly, filling of f-orbitals starts two shells after the filling of d-orbitals begin. The first element where f-orbitals \((5f)\) start filling is Actinium \((Ac)\) with atomic number \(89\).

Following the same logic, g-orbitals would be expected to start filling two shells after the filling of f-orbitals begins.

Since Actinium \((Ac)\) has an atomic number of 89, adding two shells (which means going 18 elements further twice) would lead us to element \(89 + (2 × 18)\) = 125.

However, there's a theoretical concept of electron configuration beyond filling the 7th shell (where Actinium resides). This theoretical concept suggests the existence of elements beyond the periodic table, called superactinides. The first element in this category would be Ununbium (Uub) with an atomic number of \(121\).

Therefore, based on the expected pattern of filling orbitals and the concept of superactinides, the filling of g-orbitals is likely to begin at element \(121\) (Ununbium).

It's important to note that superactinides haven't been synthesized yet and their existence is purely theoretical.