Answer:-

The ground-state electronic configurations of gadolinium (Gd) and lawrencium (Lr) differ from what might be expected based on simple electron filling rules due to the influence of electron-electron repulsions and relativistic effects.

1. Gadolinium (Gd): Gadolinium has an atomic number of 64, which would suggest that its ground-state electron configuration should follow the filling order of electrons in a neutral atom: 1s² 2s² 2p⁶ 3s² 3p⁶ 4s² 3d¹⁰ 4p⁶ 5s² 4d¹⁰ 5p⁶ 6s² 4f⁷ 5d¹. According to this filling order, the 4f orbitals should be half-filled with seven electrons.

   However, in the actual ground-state electronic configuration of gadolinium, it is found that the 4f orbitals are completely filled with seven electrons (4f⁷) instead of being half-filled (4f⁵), as might be expected. This deviation from the expected filling order occurs because having a half-filled 4f subshell would lead to higher electron-electron repulsions, making it less stable. The electronic configuration with a fully-filled 4f subshell (4f⁷) results in lower energy and greater stability due to reduced electron-electron repulsions.

2. Lawrencium (Lr): Lawrencium has an atomic number of 103, and its ground-state electron configuration is influenced by relativistic effects, which become significant for heavy elements with high atomic numbers. Relativistic effects cause contraction of the inner electron orbitals and an increase in the effective nuclear charge experienced by the outermost electrons.

   As a result of relativistic effects, the 7s and 5f orbitals of lawrencium are filled before the 6d orbitals, contrary to the expected filling order based solely on the periodic table. The actual ground-state electron configuration of lawrencium is: 1s² 2s² 2p⁶ 3s² 3p⁶ 4s² 3d¹⁰ 4p⁶ 5s² 4d¹⁰ 5p⁶ 6s² 4f¹⁴ 5d¹⁰ 6p⁶ 7s² 5f¹⁴ 6d¹⁰ 7p¹. This configuration is a result of the influence of relativistic effects on the electronic structure of heavy elements like lawrencium.

In summary, the ground-state electronic configurations of gadolinium and lawrencium differ from what might be expected based solely on the periodic table due to considerations of electron-electron repulsions (in the case of gadolinium) and the significant influence of relativistic effects (in the case of lawrencium) on the electronic structure of these elements. These factors lead to more stable electronic configurations that deviate from simple electron filling rules.