Chapter Two: Quantum Mechanical Model of an Atom Overview

Quantum theory

Study of matter at subatomic levels.

Electromagnetic radiation

Wave of oscillating electric and magnetic fields.

Photoelectric effect

Emission of electrons when light hits a material.

Line spectra

Discrete wavelengths emitted by atoms.

Bohr model

Early atomic model focusing on electron orbits.

Quantum Mechanical model

Explains electron behavior in atoms.

Quantum numbers

Set of values describing electron properties.

Atomic orbitals

Regions where electrons are likely found.

Wavelength (λ)

Distance between corresponding points on waves.

Frequency (ν)

Number of waves passing a point per time.

Speed of light (c)

Constant at 3.00 x 10^8 m/s.

Constructive interference

Waves combine to form a larger wave.

Destructive interference

Waves cancel each other out.

Diffraction

Bending of waves around obstacles.

Subatomic particles

Electrons, protons, and neutrons in matter.

Reactive elements

Elements that readily undergo chemical reactions.

Inert elements

Elements that do not readily react.

Helium-Neon laser

Emits red light at 632.8 nm wavelength.

Cell phone frequency

Uses 835.6 MHz for communication.

Periodic table trends

Patterns in element properties based on electron behavior.

Chemical bonding

Attraction between atoms forming compounds.

Photoelectric effect

Electrons emitted when light strikes metal surface.

Threshold frequency

Minimum frequency for electron emission regardless of intensity.

Work function (Φ)

Energy needed to dislodge an electron from metal.

Kinetic energy of electrons

KEelectron = hν - Φ, where h is Planck's constant.

Photon

Quantum of electromagnetic radiation with energy hν.

Emission spectrum

Unique light pattern emitted by excited atoms.

Line spectra

Non-continuous spectra identifying specific elements.

Continuous spectrum

Unbroken range of wavelengths, like white light.

Atomic spectroscopy

Technique to identify elements using emission spectra.

Flame tests

Method to identify elements via color in flames.

Bohr model

Atomic model with quantized electron orbits.

Stationary states

Fixed electron orbits around the nucleus.

Energy quantization

Energy levels in an atom are discrete.

De Broglie wavelength

Wavelength associated with a particle's mass and velocity.

Matter waves

Wavelike behavior of particles proposed by De Broglie.

Electromagnetic radiation

Energy waves including visible light and others.

Energy of a photon

E = hν, where E is energy, h is Planck's constant.

Energy of 1 mole of photons

Multiply energy of one photon by Avogadro's number.

Laser pulse energy

Total energy contained in a laser pulse.

Frequency (ν)

Number of cycles per second of a wave.

Wavelength (λ)

Distance between consecutive peaks of a wave.

Ionization energy

Energy required to remove an electron from an atom.

DeBroglie Wavelength

Wavelength associated with a moving particle.

Electron Diffraction Pattern

Interference pattern showing electron wave nature.

Wave Duality

Electrons exhibit both wave and particle characteristics.

Interference Pattern

Pattern formed by overlapping waves.

Heisenberg's Uncertainty Principle

Position and velocity uncertainties are inversely proportional.

Complementary Properties

More knowledge of one property reduces knowledge of another.

Electron Energy

Kinetic energy related to electron position.

Kinetic Energy Formula

KE = ½mv², where m is mass.

Schrödinger Equation

Equation incorporating wave-particle duality of electrons.

Wavefunction (Ψ)

Describes all information about an electron.

Orbital

Region of high probability for finding an electron.

Quantum Numbers

Set of numbers defining electron's state.

Principal Quantum Number (n)

Indicates energy level and size of orbital.

Energy Level Formula

En = -2.18 × 10⁻¹⁸ J (1/n²).

Angular Momentum Quantum Number (l)

Determines shape of the orbital.

s-Orbital

Spherical shape, l = 0.

p-Orbital

Dumbbell shape, l = 1.

d-Orbital

Four-leaf clover shape, l = 2.

f-Orbital

Eight balloons shape, l = 3.

Multi-Electron Systems

Require approximations to solve Schrödinger's equation.

High Probability Region

Area where electron is likely to be found.

Wave Function Squared (Ψ²)

Defines the probability density of finding an electron.

Magnetic Quantum Number (ml)

Describes orbital orientation; values from -l to +l.

Spin Quantum Number (ms)

Indicates electron spin; +½ or −½ values.

Principal Energy Level (n)

Indicates the energy level of an electron.

Sublevel (l)

Defines shape of orbitals; values from 0 to n-1.

Orbital

Region where an electron is likely found.

Subshell

Group of orbitals with same n and l values.

Energy Level Count

Number of sublevels equals n; orbitals = n².

Orbital Count in Sublevel

Number of orbitals = 2l + 1.

Hydrogen Emission Spectrum

Photon energy equals difference between electron states.

Probability Density (ψ²)

Probability of finding an electron at a point.

Radial Distribution Function

Total probability of finding an electron at distance r.

Node

Point where probability density drops to zero.

s Orbital (l=0)

Spherical shape; one orbital per principal energy state.

p Orbitals (l=1)

Dumbbell shape; three orbitals oriented along axes.

d Orbitals (l=2)

Five orbitals; complex shapes, some aligned with axes.

f Orbitals (l=3)

Seven orbitals; complex shapes, often eight-lobed.

Phase of an Orbital

Sign of wave function; affects orbital interaction.

Emission Spectrum Line

Represents energy transition between electron states.

Electron Relaxation

Electron emits light when transitioning to lower energy.

Quantum Number Set

n, l, ml define unique orbital characteristics.

Energy Transition Requirement

Electron must gain specific energy to move states.

Principal Shell

Another term for principal energy level.

Subshell Type

Also known as subshell; defined by n and l.