Atomic Structure and Periodic Table Trends

Electron Configurations of Selected Elements

• 1: 1s¹ (H) (1)
• 2: 2s² (Be) (2)
• 3: 3d¹ 4s² (Sc) (4)
• 4: 3d² 4s² (Ti) (4)
• 5: 3d³ 4s² (V) (4)
• 6: 3d⁵ 4s¹ (Cr) (4)
• 7: 3d⁵ 4s² (Mn) (4)
• 8: 3d⁶ 4s² (Fe) (4)
• 9: 3d⁷ 4s² (Co) (4)
• 10: 3d⁸ 4s² (Ni) (4)
• 11: 3d¹⁰ 4s¹ (Cu) (4)
• 12: 3d¹⁰ 4s² (Zn) (4)
• 13: 2s² 2p¹ (B) (2)
• 14: 2s² 2p² (C) (2)
• 15: 2s² 2p³ (N) (2)
• 16: 2s² 2p⁴ (O) (2)
• 17: 2s² 2p⁵ (F) (2)
• 18: 1s² (He) (1)

Atomic Mass and Spectra Formulas

Atomic mass: (Total mass of isotope × abundance %) / 100 (in grams/atoms).

Wave Relations: c = λ × ν | E = h × ν

Atomic spectra: 1 / λ = R (1.097 × 10⁷) × (1 / n₁² - 1 / n₂²)

Frequency (ν): ν = E / h | Wavelength (λ): λ = c / ν

Electron Affinity

Electron Affinity is defined as the energy that a neutral gaseous atom in its ground state delivers when it captures an electron and becomes the corresponding mononegative gaseous anion. The smaller the atom, the closer the captured electron comes to the nucleus, and therefore it will be retained with more force. Thus, moving down a group will decrease the electron affinity, while it increases moving to the right across a period.

Quantum Number Examples

Example: (3, 1, 0, 1/2)

• n = 3: 3rd energy level.
• L = 1: p sublevel.
• M = 0: 3p_y orbital.
• S = 1/2: Spin directed upwards.

Definitions:

• N: The energy level.
• L: Sublevels (n=3: 0, 1, 2 = s, p, d).
• M: Orbitals (-1, 0, +1 = P_x, P_y, P_z).
• S: Spin; positive (upwards) or negative (downwards).

Periodic Properties

Atomic Radius and Atomic Volume

As we go down a group from one element to the next, additional shells of electrons are interspersed. Thus, electrons are increasingly farther from the nucleus, which leads to an increase in the radius and volume. As we advance in a period from left to right, we move within the same quantum level; the distance from the nucleus to the outer layer is similar in all elements of the period. However, as you move from one atom to the next by adding a proton to the nucleus and an electron to the crust, the attractive force (Coulomb's Law) will intensify. This results in a gradual diminution of the atomic radius and volume.

Ionization Energy

Ionization Energy is exactly the energy required to remove an electron from a neutral, gaseous atom in its base state to make it the corresponding monopositive gaseous cation. The larger the atom, the farther the electron is from the nucleus, and therefore less energy will be needed to ionize said atom. (Size ↑, Ionization Energy ↓). Ionization energies are measured in Joules (J). Elements that form cations easily are metals; these metals are said to be electropositive.