ch 8

Dual Nature of Light: Light exhibits both wave-like and particle-like properties.
Relationships:
- Wavelength (): Distance between two corresponding points on a wave.
- Frequency (v): Number of wave crests passing a point per second; measured in hertz (Hz) or s.g, s.g, s.g, s.g
Constant Relationship:
- Equation relating wavelength, frequency, and speed of light:
  $v ext{(wavelength)} imes ext{(frequency)} = c$
- Speed of light (c): $c = 2.998 imes 10^8 m/s$
- Units: m/s can also be written as m.s.g

Light is a form of energy characterized as a moving wave of electrical and magnetic potential.
Complete Definitions:
- Wavelength (): Distance between successive crests of a wave.
- Frequency (v): The count of wave crests that pass a specified point per second, expressed in hertz (Hz).

Definition: The electromagnetic spectrum encompasses all types of electromagnetic radiation, which include:
- Radio waves
- Microwaves
- Infrared light
- Visible light
- Ultraviolet light
- X-rays
- Gamma rays
Energy Relationship: Long wavelengths correspond to low frequencies and low energy (e.g., radio waves), while short wavelengths correspond to higher frequencies and higher energy (e.g., X-rays).

Energy spectrum illustrated showing various types of light from low (radio waves) to high (gamma rays) energy.

Radio waves: Wavelength $ext{(m)} = 10^3$ , Frequency ext{(s}.g) = 3 imes 10^5
Microwaves: Wavelength $10^{-2}$ , Frequency $3 imes 10^{10}$
Infrared Light: Wavelength $10^{-5}$ , Frequency $3 imes 10^{13}$
Visible Light: Wavelength $4.0 imes 10^{-7} ext{to } 7.5 imes 10^{-7}$ , Frequency $4 imes 10^{14} ext{to } 7.5 imes 10^{14}$
Ultraviolet Light: Wavelength $10^{-8}$ , Frequency $3 imes 10^{16}$
X-rays: Wavelength $10^{-10}$ , Frequency $3 imes 10^{18}$
Gamma rays: Wavelength $10^{-12}$ , Frequency $3 imes 10^{20}$

Light Absorption: When an atom absorbs light energy from its environment, it gains energy.
Light Emission: Occurs when an atom that has excess energy releases it by emitting light. The specific wavelengths emitted by an atom correspond to its absorption capabilities, creating a unique absorption spectrum for each element.

General Summary: Light can behave as a wave or as particles (photons). In experiments, shining light on a metal surface will eject electrons if the light meets a minimum (threshold) energy requirement.
Key Points:
- The brightness of the light refers to the number of photons emitted (related to number of electrons ejected), not the energy of individual photons.
- This phenomenon is known as the photoelectric effect, with emitted electrons termed photoelectrons.

Niels Bohr's model (Nobel Prize 1921): Light is composed of packets, or photons, that can knock electrons off surfaces if they contain enough energy.

Light demonstrates characteristics of both waves and particles, summed up in:
- $E = hv$ where E = energy, h = Planck's constant ( $6.626 imes 10^{-34} J ext{· s}$ ), and v = frequency.

Absolute minimum energy required to eject an electron from the surface of a metal: denoted as Φ.
- Relation: $hv = ext{Φ}$ .
- The wavelength can be derived from the frequency: $\frac{hc}{ ext{Φ}}$ .

Excess energy of the impacting photon converts to the kinetic energy of the ejected electron:
- Kinetic energy representation: $ext{KE} = hv - ext{Q}$ where Q is the work function.

Describes how energy levels in atoms lead to light emission and absorption processes of gaseous atoms.
Light emission is distinct to gaseous atoms when heated, evidenced by unique emission spectra; contradicts Rutherford's free-electron model.

Proposition: Electrons occupy specific distances (orbits) around the nucleus, in defined energy levels.
- Ground state: Lowest energy level closest to the nucleus; Excited states: Higher levels generated by energy absorption leading to light emission.

Concentrating on hydrogen's emission spectrum:
- $\frac{1}{ ext{λ}} = R_H\bigg( \frac{1}{n^2_1} - \frac{1}{n^2_2} \bigg)$ where $R_H = 1.097 imes 10^7 m^{-1}$ .
- Energy transition formula allows calculation of light's emitted photon energy: $E = \frac{2.179 imes 10^{-18} J}{n^2}$ .

Description of electron distribution and arrangement around the nucleus of atoms captured through Quantum mechanical model:
- De Broglie: Matter possesses both wave-like and particle-like properties, leading to the Heisenberg uncertainty principle.
Electrons: Not occupying fixed orbits, but cloud-like orbitals with uncertain positions and velocities as captured by Schrödinger's wave equation.

Orbitals: 3D probability distributions for where electrons likely reside.
Subshells: Groups of orbitals with equivalent energy levels (s, p, d, f).
Electron Shells: Principal energy levels composed of subshells with hierarchical structure dependent on distance from nucleus.

Shapes and Sizes:
- s orbital: Spherically symmetrical.
- p orbital: Has three orientations with two lobes each.
Sizes increase with higher energy levels of orbitals.

Purpose: Illustrate electronic configurations showing the hierarchy of subshells and the filling method of electrons.
Pauli Exclusion Principle: No two electrons in an atom can possess identical sets of quantum numbers, which dictate electron arrangement.
Hund’s Rule: Within a subshell, electrons prefer to remain unpaired as much as possible, occupying different orbitals first.

The arrangement of electrons, shown as a combination of energy level and subshell type, often represented with subscripts indicating the number of electrons in each subshell:
- Notation Example: For oxygen: $1s^2 2s^2 2p^4$ indicating 8 total electrons in its configuration.
Abbreviated Configurations: Represented with noble gas symbols; for instance, lead (Pb) written as $[Xe]6s^24f^{14}5d^{106}p^2$ .

Four quantum numbers:
- Principal Quantum Number (n): Indicates energy level
- Angular Momentum Quantum Number (ℓ): Related to subshell type
- Magnetic Quantum Number (mℓ): Specifies the orbital within a subshell
- Spin Quantum Number (ms): Indicates the spin direction of the electron.
Pauli Exclusion Principle: Asserts distinct quantum numbers for each electron in an atom.