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Chapter 2: Atomic Structure and Periodicity

Read chapter sections 2.1 to 2.11.
Start C11_Hw 3 today and finish by Tuesday (2/4).
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Each orbit has a specific amount of energy.
Energy of each orbit is characterized by an integer:
- Larger integer = higher energy; E = 0 at n = infinity.
- More positive energy indicates the electron is farther from the nucleus.
- Integer, n, is called the shell or energy level number.
- Lowest energy (n=1) is called the ground state; higher states are called excited states.
Energy formula:[ E_n = -2.178 \times 10^{-18} J \frac{Z^2}{n^2} ] where Z is the atomic number.

Determine which light has the longest wavelength: n=2 to n=1 or n=3 to n=2?
Transition from n=3 to n=4:
- Closer to or further from the nucleus?
- Does the electron lose or gain energy?
- Is a photon created or destroyed?
Energy needed to ionize hydrogen atom from n=3:[ E_n = -2.178 \times 10^{-18} J \frac{1}{n_f^2} - \frac{1}{n_i^2} ] → for n_final = infinity.

Successfully predicts spectrum of hydrogen and single electron ions (e.g., He+, Li2+).
Limitations:
- Does not account for electron-electron interactions in multi-electron atoms.
- Fails to explain why only certain energies are allowed.
- Cannot explain why the electron doesn't crash into the nucleus due to energy loss.
Wave-particle duality: Light behaves both as a wave and a particle, similar to electrons.
Heisenberg Uncertainty Principle: ( \Delta x \Delta mv \ge h/(4\pi) \)

Light and electrons exhibit both wave-like and particle-like characteristics.
The idea of orbitals modifies Bohr's theory, introducing electron-waves instead of fixed orbits.

De Broglie's hypothesis: matter possesses wave properties.
Development of quantum mechanics by Born, Schrödinger, and Heisenberg incorporates wave and particle nature.
Electron-wave described by wave function (( \Psi )), with its likelihood location represented by ( \Psi^2 ).
Graphs and shapes illustrate orbitals, indicating probabilities of finding electrons at certain locations.

Replace Bohr orbits with orbitals, maintaining energy similarities for hydrogen.
For various n levels, energy increases relate to:
- Number of nodes (zero probability areas)
- Wavelength and frequency
- The probable location of the electron, analyzed via ( \Psi^2 ) for probability estimates.

Orbital shapes: s, p, d, f, etc.
- p-orbitals contain one angular node.
- Total nodes = n - 1.
Quantum Numbers (Pauli’s exclusion principle):
1. Principal quantum number (n): Energy levels (shells).
2. Angular momentum quantum number (l): Describes shapes (sub-shells); ranges from 0 to n-1, represented as s, p, d, f.
3. Magnetic quantum number (ml): Orientation of orbital, ranging from -l to +l.
4. Spin quantum number (ms): Electron spin (± ½).

Subshell energies differentiated by electron interactions and penetration effects:
- Energy ranking: s < p < d < f.
Aufbau principle: Orbits fill from low to high energy.
- Maximum of two electrons per orbital, which must have opposite spins.
- Hund’s Rule: Equal energy orbitals filled singly before pairing.

Ground state orbital diagram and electron configuration for Mg (Z=12):
- Diagram shows filling order by energy.
- Follow Aufbau rules to determine configurations for ions like Mg2+ or Mn.