atomic structure

Overview of Atomic Structure

  • Atoms compared to college housing
      - Multiple Floors: Each floor corresponds to an electron shell.
      - Apartments (subshells): Some are fancier with more rooms (orbitals).
      - Orbitals: Each orbital can fit a maximum of two electrons.

Quantum Numbers

Definition of Quantum Numbers

  • Address of an Electron: Given by a set of four quantum numbers.
      - Example for an electron named Elena:
        - $n = 3$ (Principal Quantum Number)
        - $l = 1$ (Azimuthal Quantum Number)
        - $m_{l} = 0$ (Magnetic Quantum Number)
        - $m_{s} = - rac{1}{2}$ (Spin Quantum Number)

Principal Quantum Number (n)

  • Represents the energy level of an electron.
  • Building Krypton has 4 floors (electron shells).
      - Elena's floor: 3rd (since $n = 3$).

Azimuthal Quantum Number (l)

  • Represents the type of subshell (apartment) in which the electron resides.
  • Subshell types:
      - $l = 0$: s subshell (spherical shape)
      - $l = 1$: p subshell (dumbbell shape)
      - $l = 2$: d subshell (clover shape)
      - $l = 3$: f subshell (complex shape)
  • Formula to determine possible subshells:
    l=n−1l = n - 1
  • For $n = 3$, possible $l$ values: $0, 1, 2$ (s, p, d subshells).
      - Since $l = 1$, Elena is in the p subshell.

Magnetic Quantum Number (m_{l})

  • Determines the number of orbitals in a subshell.
  • For a given $l$, the possible values for $m_{l}$ range from $-l$ to $+l$.
  • If $l = 1$ (p subshell), then $m_{l}$ can be $-1, 0, +1$:
      - Three orbitals in the p subshell.
      - Since $m_{l} = 0$, Elena is in the middle orbital (0).

Spin Quantum Number (m_{s})

  • Indicates the spin direction of the electron.
  • Can only be:
      - $+ rac{1}{2}$ or $- rac{1}{2}$.
  • Electrons with opposite spins can coexist due to repulsion being canceled out.

Special Properties of Subshells

Orientation of Different Subshells

  • s subshell:
      - $l = 0$ → 1 orbital → $m_{l} = 0$ ∎ 1
  • d subshell:
      - $l = 2$ → 5 orbitals → $m_{l} = -2, -1, 0, +1, +2$
  • f subshell:
      - $l = 3$ → 7 orbitals → $m_{l} = -3, -2, -1, 0, +1, +2, +3$

Pauli's Exclusion Principle

  • No two electrons can have the same set of quantum numbers.
  • This aligns with how students occupy unique spaces and don't overlap each other.

Electron Configuration

Understanding Electron Configuration

  • Unique configurations for each element found via the periodic table.
  • Atomic structure denotes the arrangement of electrons in subshells based on quantum numbers.
  • Building Krypton’s Electron Configuration:
      - First energy level ($n=1$): 2 electrons in $1s$
      - Second energy level ($n=2$): 2 in $2s$, 6 in $2p$
      - Third energy level ($n=3$): 2 in $3s$, 6 in $3p$, 10 in $3d$
      - Fourth energy level ($n=4$): 2 in $4s$, 6 in $4p$

Notation of Electron Configuration

  • Coefficients denote energy levels, letters for subshells, and superscripts for electron count.
  • Electron Configuration of Krypton:
      - 1s2ext2s2ext2p6ext3s2ext3p6ext4s2ext3d10ext4p61s^2 ext{ } 2s^2 ext{ } 2p^6 ext{ } 3s^2 ext{ } 3p^6 ext{ } 4s^2 ext{ } 3d^{10} ext{ } 4p^6
  • Shorthand notation involves referring to the last noble gas before krypton.

Paramagnetism and Diamagnetism

Diamagnetic vs. Paramagnetic

  • Krypton is diamagnetic: All electrons paired in orbitals.
  • Bromine's configuration highlights an atom with unpaired electrons:
      - 4p54p^5 indicates one unpaired electron.
  • An atom with unpaired electrons is paramagnetic.

Building Rules for Electron Arrangement

  • Aufbau Principle: Electrons fill lower energy levels before higher ones.
  • Hund's Rule: Electrons fill orbitals singly before pairing up.

Conclusion

  • Each electron in an atom has a unique address with a set of four quantum numbers.
  • Utilize the periodic table as a guiding map to locate electrons in an atom.