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)
      - $m_{s} = -\frac{1}{2}$ (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:
  $l = n - 1$
• 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:
    - $+\frac{1}{2}$ or $-\frac{1}{2}$.
• 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:
    - $1s^2 ext{ } 2s^2 ext{ } 2p^6 ext{ } 3s^2 ext{ } 3p^6 ext{ } 4s^2 ext{ } 3d^{10} ext{ } 4p^6$
• 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:
    - $4p^5$ 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.