Quantum Numbers and Electric Configuration

Quantum Numbers and Electron Configuration

Introduction to Quantum Numbers

  • Definition and Purpose

    • Quantum numbers determine the electron configuration of an atom.

    • They help in understanding characteristics like ionization energy and atomic radius.

  • Principal Quantum Number (n)

    • Can have positive integral values: 1, 2, 3, ...

    • As n increases:

      • Orbital size increases.

      • Electrons are found farther from the nucleus.

      • Higher energy and less tightly bound to the nucleus.

  • Angular Momentum Quantum Number (l)

    • Integral values from 0 to n-1.

    • Defines the shape of the orbital.

    • Corresponding letters:

      • l = 0 → s

      • l = 1 → p

      • l = 2 → d

      • l = 3 → f

  • Orbital Shape and Electron Density

    • Orbitals do not have a definite shape; wave functions extend to infinity.

    • Probability distribution shows regions where electrons are likely to be found.

    • Example: 1s orbital has a spherical probability distribution.

Orbital Types and Shapes

  • p Orbitals

    • Start at n=2 with l=1.

    • Three 2p orbitals: 2px, 2py, 2pz.

    • Shape: Double teardrop or dumbbell.

    • Zero probability along nodal planes.

  • d Orbitals

    • First appear at n=3.

    • Have two angular nodes.

    • Exhibit positive and negative lobes along axes.

    • Example: dx2 has a donut shape along the x-axis.

  • Magnetic Quantum Number (ml)

    • Integral values between -l and l, including zero.

    • Describes the orientation of the orbital in space.

  • Electron Spin Quantum Number (ms)

    • Describes the spin of an electron.

    • Electrons are paired with opposite spins, neutralizing magnetic effects.

    • Unpaired spins create a magnetic moment.

Electron Configuration

  • Hydrogen Example

    • Ground state electron configuration: 1s¹.

    • Quantum numbers: (n=1, l=0, ml=0, ms=½ or -½).

  • Electron Configuration Representation

    • Shows distribution of electrons among atomic orbitals.

    • Orbital diagram illustrates electron spin.

  • Rules for Writing Electron Configuration

    • Pauli Exclusion Principle

      • No two electrons can have the same four quantum numbers.

      • Maximum of two electrons per orbital with opposing spins.

Stability and Energy in Electron Configuration

  • Hund’s Rule

    • Most stable arrangement has the most parallel spins.

    • Example: Carbon's configuration is 1s² 2s² 2p².

    • Different arrangements yield different energy values; lowest energy is most stable.

  • Magnetic Properties

    • Paramagnetic Materials: Contain unpaired electrons, attracted to magnets.

    • Diamagnetic Materials: Have paired spins, repelled by magnets.

    • Example: Helium (diamagnetic) vs. Lithium (paramagnetic).

  • Aufbau Principle

    • Electrons fill atomic orbitals from lowest to highest energy.

    • Order of filling: s < p < d < f.

    • Filling order for multi-electron atoms is systematic.

  • Activity Suggestion

    • Engage in exercises to apply knowledge of