3.7 Orbital Electronic Configuration of Atoms

• Bohr Model & Principal Energy Levels:

• The Bohr model defines energy levels in atoms. Each energy level can contain up to 2n² electrons, where n represents the principal energy level (n = 1, 2, 3, etc.).

• Energy Level K (n = 1): 2n² = 2 electrons.

• Energy Level L (n = 2): 2n² = 8 electrons.

• Energy Level M (n = 3): 2n² = 18 electrons.

• Energy Level N (n = 4): 2n² = 32 electrons.

• Electron Configuration Examples:

• Hydrogen (H, atomic number 1): 1 electron, fills K-shell (2 electrons max).

• Helium (He, atomic number 2): 2 electrons, fills K-shell.

• Lithium (Li, atomic number 3): 3 electrons; first 2 electrons in K-shell, third in L-shell.

• Sodium (Na, atomic number 11): 11 electrons; 2 in K-shell, 8 in L-shell, 1 in M-shell.

• Electron Configuration in Higher Elements:

• For elements beyond Argon (atomic number 18), the 19th electron of Potassium (K) enters the fourth energy level (N) before the third (M) is completely filled. The 20th electron of Calcium (Ca) enters the N-shell too.

• For Scandium (Sc, atomic number 21), the 21st electron fills the M-shell after the first 2 electrons go to the N-shell.

• Concept of Energy Sublevels:

• Energy levels are further divided into sublevels (orbitals), represented by l values.

• n = 1: l = 0 → 1s (1 orbital).

• n = 2: l = 0, 1 → 2s, 2p (2 orbitals).

• n = 3: l = 0, 1, 2 → 3s, 3p, 3d (3 orbitals).

• n = 4: l = 0, 1, 2, 3 → 4s, 4p, 4d, 4f (4 orbitals).

• n = 5: l = 0, 1, 2, 3, 4 → 5s, 5p, 5d, 5f (and so on).

• The number of orbitals is given by (2l + 1), and each orbital can hold 2 electrons.

• Table: Electron Configuration in Energy Levels (n = 1-4):

• Energy Level | Orbital Symbol | Number of Electrons in Orbital | Total Electrons in Energy Level

• n = 1 | 1s | 2 | 2

• n = 2 | 2s | 2 | 8 (2 + 6)

• n = 3 | 3s, 3p, 3d | 2 + 6 + 10 | 18

• n = 4 | 4s, 4p, 4d, 4f | 2 + 6 + 10 + 14 | 32

• Principles of Electron Configuration:

• Pauli’s Exclusion Principle: No two electrons can have the same set of quantum numbers.

• Aufbau Principle: Electrons fill the lowest energy orbitals first.

• Hund’s Rule: Electrons will fill degenerate orbitals singly before pairing up.

• Energy of orbitals is determined by the sum of the principal quantum number (n) and the azimuthal quantum number (l). The orbital with a lower (n + l) value is lower in energy and fills first.

• Energy Ordering of Orbitals:

• 1s < 2s < 2p < 3s < 3p < 4s < 3d < 4p < 5s < 4d < 5p < 6s < 4f < 5d < 6p < 7s < 5f < 6d < 7p < 8s

• Orbitals have a specific order of filling due to their relative energies.

• Orbital Capacity:

• s-orbitals hold 2 electrons.

• p-orbitals hold 6 electrons.

• d-orbitals hold 10 electrons.

• f-orbitals hold 14 electrons.

• Example Configurations:

• Potassium (K, atomic number 19): 1s² 2s² 2p⁶ 3s² 3p⁶ 4s¹.

• Calcium (Ca, atomic number 20): 1s² 2s² 2p⁶ 3s² 3p⁶ 4s².

• Scandium (Sc, atomic number 21): 1s² 2s² 2p⁶ 3s² 3p⁶ 3d¹ 4s².

• Exceptions in Electronic Configuration:

• Some elements, like Chromium (Cr) and Copper (Cu), exhibit electron configurations that deviate from the expected ones due to increased stability when orbitals are half-filled or fully filled.

• Chromium (Cr, atomic number 24): Instead of 1s² 2s² 2p⁶ 3s² 3p⁶ 3d⁴ 4s², it has 1s² 2s² 2p⁶ 3s² 3p⁶ 3d⁵ 4s¹ to achieve a half-filled d-orbital for added stability.

• Key Points:

• Always check orbital filling order to avoid errors.

• Sublevels and orbitals are filled based on energy (n + l rule).

• Electronic configurations follow the principles to achieve the most stable state for the atom.