In the modern periodic table, each period starts with the filling of a new principal energy level. Thus, the third period begins with the filling of principal quantum number, n = 3. When n = 3, λ = 0, 1, 2. But according to Aufbau principle, the electrons are added to different orbitals in order of their increasing energies. Now, the energy of 3d-subshell is higher than that of 4s-subshell. Therefore, in third period, electrons can be filled in only 3s & 3p-subshells, whose energies increase in the order: 3s < 3p. Now,
s-subshell has one and p-subshell has three orbitals. Hence, in all, there are 4 (1 + 3) orbitals that can be filled in this period. Since according to Pauli's exclusion principle, each orbital, at the maximum, can accommodate two electrons. Therefore, 4 orbitals, at the maximum, can have 8 electrons and hence, fourth period has 8 elements.