All the chemical elements discovered or created so far follow a regular pattern in how their electrons are arranged: the nth shell contains up to 2n – 1 suborbitals that each contain up to two electrons. For a given atomic number, you can determine how its electrons are distributed into shells and suborbitals using the Aufbau principle.
The Aufbau principle is a good approximation, but not exact. For this post we’ll assume it is exact, and that everything in the preceding paragraph generalizes to an arbitrary number of shells and electrons.
Under those assumptions, what would the periodic table look like if more elements are discovered or created?
The number of elements in nth period works out to
and the atomic numbers of the elements at the end of the nth period (the noble gases) are
We can verify that these formulas give the right values for the actual periodic table as follows.
>>> def p(n): return ((-1)**n*(2*n+3) + 2*n*n + 6*n +5)/4 >>> def z(n): return ((-1)**n*(3*n+6) + 2*n**3 + 12*n**2 + 25*n - 6)/12 >>> [p(n) for n in range(1, 8)] [2.0, 8.0, 8.0, 18.0, 18.0, 32.0, 32.0] >>> [z(n) for n in range(1, 8)] [2.0, 10.0, 18.0, 36.0, 54.0, 86.0, 118.0]
So, hypothetically, if there were an 8th row to the periodic table, it would contain 50 elements, and the last element of this row would have atomic number 168.