College Physics Chapter 6 Notes

Electromagnetic waves exhibit particle characteristics.
Louis de Broglie suggested particle wave behavior.
Observation of wave nature leads to inability to observe particle nature (and vice versa).
- Wave nature: interference pattern.
- Particle nature: position and path (which slit does it pass through?).
These two natures are complementary; knowledge of one decreases knowledge of the other.

Fundamental equation:
- Energy relation: E = hn where h is Planck’s constant, n is the frequency.
- Relation to wavelength: E = \frac{hc}{\lambda} and E = mc^2.
Substitute to find wavelength for electrons:
- \lambda = \frac{h}{mv} where \lambda is De Broglie wavelength, m is mass, v is velocity.
Applicable to all moving particles, showing they possess wavelike properties.

Standing wave: oscillates within a fixed space.
Nodes: positions with no displacement.
Example of a standing wave corresponds to the lowest allowed wavelength in physical systems.
Harmonics described by: L = \frac{n\lambda}{2}, where n is an integer denoting harmonic.

Electrons behave as circular waves around the nucleus with stable circular patterns when wavelength fits evenly in orbits.
The circumference equals an integer multiple of the wavelength: C = n\lambda.
Minimum radius occurs at n = 1.

C. J. Davisson and L. H. Germer demonstrated electron wavelike behavior experimentally through diffraction patterns in crystals resembling light interference patterns.
This implies electrons follow wave equations rather than classical mechanics.

Introduces the limitation of knowing the position and momentum of electrons simultaneously.
- The more accurately position is known, the less accurately momentum can be measured, and vice versa.
Heisenberg applied matrix mechanics, creating matrices to describe observable properties like energy and momentum.

Both Schrödinger and Heisenberg contributed to quantum mechanics; Schrödinger developed wave functions (denoted as \Psi) to predict electron positions and energies.
Orbitals are characterized by quantum numbers:
- Principal quantum number (n): energy level and size.
- Angular momentum quantum number (l): shape of the orbital.
- Magnetic quantum number (m_l): orientation in space.
- Spin quantum number (m_s): direction of electron spin (either +1/2 or -1/2).

Orbitals are mathematical representations of probable electron locations. Each orbital is defined by three quantum numbers:
- Single subshell can hold a maximum of 2 electrons with opposite spins, obeying Pauli’s Exclusion Principle.
- The size, shape, and orientation can be determined using integer terms from the wave function. This represents the energy states available for electrons.

Different atomic orbitals (s, p, d, f) provide distinct shapes and configurations:
- s orbitals: spherical (1 orbital, can hold 2 electrons).
- p orbitals: two-lobed (3 orbitals, can hold 6 electrons).
- d orbitals: more complex shapes (5 orbitals, can hold 10 electrons).
- f orbitals: even more complex (7 orbitals, can hold 14 electrons).
Electron configurations describe how electrons are distributed across these orbitals in an atom's ground state: represented in terms of increasing energy levels and subshells.

Electron configurations are linked to periodic trends in properties such as atomic radius, ionization energy, and electron affinity.
As atomic number increases, trends emerge:
- Atomic radius decreases across a period due to increased nuclear charge pulling electrons closer.
- Ionization energy typically increases across a period as the effective nuclear charge rises, making it harder to remove electrons.
- Electron affinity reflects the energy change when an atom gains an electron, often becoming more negative across the periodic table, with notable exceptions.

Metallic character is more significant on the left side of the periodic table and decreases across a period and increases down a group.
Metals tend to lose electrons easily (form cations), while nonmetals gain electrons (form anions).
The stability and reactivity are also dependent on the electron configurations, which correlate to position in the periodic table, helping predict how atoms will behave chemically.