Study Notes: Unit 2 Matter & Energy

Unit 2: Matter & Energy

Objectives

• 2.0 The student shall be able to describe the structure and properties of matter and energy.

  • 2.1 Differentiate between matter and energy.

  • 2.2 Describe the basic structure and states of matter.

  • 2.3 Discuss the history of investigation into the atom.

  • 2.4 Describe the structure, configuration, and properties of atoms.

  • 2.5 Describe the Periodic Table of the Elements.

  • 2.6 Identify various types of energy.

  • 2.7 Differentiate between radiations along the electromagnetic (EM) spectrum.

  • 2.8 Describe wave and particle theories for EM radiation.

  • 2.9 Identify the properties of x-rays.

Matter & Energy

• Definition of Matter and Energy:

  • Matter: Anything that takes up space and has form or shape.

  • Energy: The ability to do work.

• There are various forms of matter and energy.

Properties of Matter

• Mass:

  • Mass is the quantity of matter contained in an object.

  • SI Unit of Mass: Kilogram (kg) with the conversion of 1 kilogram = 1,000 grams.

  • Mass is associated with weight, but they are not the same.

Mass Versus Weight & Gravity

• Weight:

  • The force that an object exerts under gravity.

• Gravity:

  • A force of attraction between any two masses, bodies, or particles.

  • It is dependent on mass: as mass increases, gravitational attraction increases.

• Acceleration of Gravity (g):

  • Objects fall to Earth at a constant rate, defined as:

  • $g_{Earth} = 9.8 ext{ m/s}^2$ (approx. 32 feet per second)

  • $g_{Moon} = 1.6 ext{ m/s}^2$

  • $g_{Jupiter} = 24.8 ext{ m/s}^2$

• Example of Changing Weight:

  • A person with a mass of 91 kg (approx. 200 lbs.) weighs approximately 32 lbs. on the moon and about 473 lbs. on Jupiter due to differing gravities.

  • Weight changes with gravity while mass remains constant.

What is Matter Made of?

• Ancient Beliefs:

  • Ancient Greeks proposed four elements: fire, air, water, and earth.

  • Aristotle (384-322 BC):

  • Believed matter can be divided indefinitely.

  • Democritus (460-370 BC):

  • Suggested matter consists of tiny particles called "atomos" (indivisible).

• The atomic theory did not prevail until the early 1800s when scientists confirmed that atoms are the building blocks of matter.

Structure of Matter

• Matter commonly exists as a mixture of substances:

  • Substances: Materials with a definite & constant composition.

  • Simple Substances - Elements: Cannot be broken down further.

  • Atoms: Smallest particle of an element, e.g., silver (Ag) made up of silver atoms.

  • Complex Substances - Compounds: Formed from two or more different elements chemically combined.

  • Molecules: Combinations of two or more atoms, e.g., H2O (water molecule).

Basic States of Matter

• Solids:

  • Fixed volume and shape.

  • Molecules are tightly packed and primarily vibrate.

• Liquids:

  • Defined volume but undefined shape.

  • Molecules are close but can move past each other, filling the container shape.

• Gases:

  • Indefinite volume and shape; molecules are far apart, move freely, and compress easily.

History of Atomic Theory

• John Dalton (1808):

  • Differentiated elements by mass; atoms of an element react uniformly.

• Dmitri Mendeleev (1869):

  • Created the Periodic Table arranging elements by atomic mass and chemical properties.

• Ernest Rutherford (1911):

  • Developed the nuclear model of the atom structure with a positively charged nucleus and surrounding electrons.

• Niels Bohr (1913):

  • Proposed a model describing electrons in fixed orbits around the nucleus.

• Erwin Schrödinger (1926):

  • Introduced the concept of orbitals as probabilities for electron locations, forming the basis of quantum mechanics.

Atomic Structure

• Nucleus:

  • Dense center of the atom containing nucleons (protons & neutrons).

• Orbitals:

  • Electrons occupy defined energy levels surrounding the nucleus.

• Variation in atomic structure includes differences in nucleon and electron counts.

Protons & Neutrons

• Protons:

  • Positively charged particles with mass $1.673 imes 10^{-27} ext{ kg}$.

  • The number of protons determines the element type.

  • Example: Sodium (Na) has 11 protons; if it had 12, it would become Magnesium (Mg).

• Neutrons:

  • Uncharged particles with mass $1.675 imes 10^{-27} ext{ kg}$.

  • Individual neutrons have consistent mass across atoms.

Electrons

• Electrons:

  • Negatively charged particles with mass $9.109 imes 10^{-31} ext{ kg}$.

  • Constantly in motion around the nucleus, with energy levels determining their orbits.

  • Binding Energy (Eb):

  • Energy needed to remove an electron, measured in electron volts (eV).

  • SI unit for binding energy is the electron volt (eV).

  • $1 ext{ keV} = 1,000 ext{ eV}$.

Quarks & String/M Theory

• Quarks:

  • Sub-nuclear structures comprising protons and neutrons, typically existing in groups of three.

• String Theory:

  • Proposes that quarks and electrons are not particles but small vibrating strings.

  • M Theory:

  • Aims to unite quantum physics with relativity.

Atomic Mass

• Majority of atom mass derives from nucleons, as they are significantly larger than electrons.

  • Neutron mass compared to electron: 1,838 times larger.

  • Proton mass compared to electron: 1,836 times larger.

• The contribution from orbital electrons is negligible when calculating atomic mass.

  • Example:

  • Hydrogen (H) with one proton vs. silver (Ag) having 47 protons and 61 neutrons.

Atomic Mass Number

• Expresses the total number of nucleons (protons + neutrons) in an atom, referenced relative to carbon-12 when precision is not crucial.

  • Protons & neutrons approximately 1 mass unit each; electrons effectively contribute zero to atomic mass.

• Example Atomic Notation:

  • $^{40}_{20}Ca$

  • 20 = Atomic Number (Z - protons).

Isotopes

• Differ in neutron count while maintaining atomic number (element identity).

  • Man-made isotopes created through particle additions/removals require specialized equipment.

  • Radioisotopes:

  • Unstable isotopes emitting radiation, possibly man-made.

Example of Isotopes

• Hydrogen Isotopes:

  • Protium (Hydrogen-1): Most prevalent, stable, 99.985% of hydrogen.

  • Deuterium (Hydrogen-2): Less common, stable, 0.015% of hydrogen.

  • Tritium (Hydrogen-3): Unstable, radioactive, minimal existence.

Electron Orbitals

• Atoms must have at least one energy shell to exist, e.g., hydrogen.

• Maximum of 7 electron shells present in an atom, represented by letters (K, L, M, N, O, P, Q).

• Forces Maintaining Electron Motion:

  • Centrifugal force (tending to fling electrons away) and electrostatic force (positive nucleus attracting negative electrons).

Electron Distribution

• Different atoms have varying electron counts in energy shells.

• Maximum Electron Occupancy Formula:

  • $2n^2$, where n = principal quantum number.

• Example Calculation:

  • Maximum electrons in L-shell (n=2) = $2(2^2) = 8$.

• Outermost Shell (Octet Rule): - Maximum of 8 electrons can occupy the outermost shell, but atoms with one shell can have 2.

Electrical Stability

• Typically, electrically neutral atoms will have equal protons and electrons.

• Imbalances occur during chemical bonding or exposure to ionizing radiation.

Electron Binding Energies

• Binding energy (Eb) required to remove an electron from an atom.

  • Higher binding energy occurs for electrons closer to the nucleus.

• Example: - K-shell electrons require 1072 eV to eject; outer M-shell electrons only require 1 eV.

Periodic Table of the Elements

• Graphical organization of known elements by atomic number and grouped by chemical properties.

  • Each box contains:

  • Chemical symbol.

  • Atomic number above the symbol.

  • Atomic weight (average of isotopes) below the symbol; may not be a whole number.

• Element Count:

  • 92 naturally occurring elements with many others synthesized in labs.

  • Elements are generally rare; 95% of Earth and atmosphere consist of about a dozen elements.

  • 99% of human body mass is composed of oxygen, carbon, hydrogen, nitrogen, calcium, and phosphorus.

Periodic Table Arrangement

• Vertical Columns (Groups):

  • Represent the number of electrons in outer shell.

• Horizontal Rows (Periods):

  • Indicate the number of energy shells (orbitals) present.

Valence

• Valence is determined by the number of electrons in the outermost shell of an atom.

  • Atoms with 8 electrons in the outer shell are stable and non-reactive.

  • Atoms with less than 8 electrons are more reactive.

• Valence Example:

  • Hydrogen (1 electron in its outer shell, valence = +1).

  • Iodine (7 electrons, valence = -1).

Changes to Atomic Configuration

• Adding/Removing Protons: Changes element type.

  • Example:

  • $^{12}C + 1 ext{ proton} = {^{12}/N}$ (Nitrogen)

• Adding/Removing Neutrons: Creates isotopes of the same element.

  • Example:

  • $^{12}C + 1 ext{ neutron} = {^{13}C}$ (Carbon-13)

• Adding/Removing Electrons: Creates ions.

  • Positive Ion: More protons than electrons.

  • Negative Ion: More electrons than protons.

Ionization

• Adding or removing an electron from an atom's shell, requiring external energy input (e.g., x-radiation, gamma rays).

• Electron Binding Energy: Indicates energy needed to remove an electron; highest energy needed for K-shell, lowest for outermost shell.

  • Energy required for K-shell is 1072 eV; for outer M shell, about 1 eV.

Properties of Energy

• Definition of Energy: The capacity to perform work, resulting from force acting over a distance.

  • Formula for Work: $ext{Work} = ext{Force} imes ext{Distance}$

  • SI Unit of Energy: Joule (J).

• Energy transmitted through matter is radiation.

Types of Energy

• Mechanical Energy:

  • Related to machines and physical actions, including potential and kinetic energies.

• Chemical Energy:

  • Released during chemical reactions; examples include batteries, petroleum, and food.

• Thermal Energy:

  • Energy from moving atoms and molecules; temperature reflects this energy level.

• Electrical Energy:

  • Results from moving electrons.

• Nuclear Energy:

  • Released from atomic nuclei reactions (fusion or fission).

• Electromagnetic Energy:

  • Electric and magnetic disturbances traveling in space.

Mechanical Energy

• Involves machines or physical motion, segmented as:

  • Potential Energy: Stored energy due to position.

  • Kinetic Energy: Energy of motion.

Chemical & Thermal Energy

• Chemical Energy:

  • Released by chemical reactions (e.g., batteries, fuels).

• Thermal Energy (Heat):

  • Produced by moving particles; higher movement indicates higher thermal energy.

Electrical Energy

• Result from the flow of electrons (kinetic energy); used in appliances and machines.

Nuclear Energy

• Energy released from reactions involving atomic nuclei:

  • Fusion: Combining of nuclei, releasing energy.

  • Example: Sun fuses hydrogen into helium.

  • Fission: Splitting of nuclei, such as uranium atoms, producing energy or radiation.

  • Used in nuclear weapons.

Electromagnetic Energy

• Electric and magnetic disturbances propogating through space at the speed of light ($c = 3 imes 10^8 ext{ m/s}$).

• Types include:

  • Radiowaves

  • Microwaves

  • Infrared Radiation

  • Visible Light

  • Ultraviolet Radiation

  • X-rays and Gamma Rays

Representing EM Radiations

• EM radiations are described as energy bundles called photons; represented via sine waves:

  • Amplitude: Maximum height of the wave, indicating energy intensity.

  • Wavelength (λ): Distance between successive points on a wave.

  • Ranges from kilometers to Angstroms (Å = $10^{-10} ext{ meters}$).

  • Short wavelengths: higher energy.

  • Example: Wavelengths of x-ray photons fall between 0.1 to 0.5 Å.

Frequency

• Frequency (ν or f): Number of waves passing a point in a time frame; measured in Hertz (Hz = cycles per second).

  • Period = Time for one complete cycle.

• Direct correlation between frequency/energy (high frequency = high energy) and an inverse relationship with wavelength (short wavelength = high energy).

Calculating Frequency

• Frequency Calculation Example:

  • If 240 wavelengths pass in 30 seconds:

  • Frequency = $240 / 30 = 8 ext{ Hz}$.

Wave Theory

• The frequency-wavelength relationship is inversely proportional as expressed by the wave equation:

  • $c = v imes ext{λ}$

  • $ext{λ} = c/v$

  • $v = c/ ext{λ}$

Calculating Frequency & Wavelength

• Example Frequency Calculation:

  • Photon wavelength of $2.5 imes 10^3 ext{ m}$:

  • $v = c/ ext{λ} o v = 3.0 imes 10^8 / 2.5 imes 10^3 = 1.2 imes 10^5 ext{ Hz}$.

• Example Wavelength Calculation:

  • Photon with frequency $1.6 imes 10^5 ext{ Hz}$:

  • $ext{λ} = c/v o ext{λ} = 3.0 imes 10^8 / 1.6 imes 10^5 = 1.875 imes 10^3 ext{ m}$.

The EM Spectrum

• Definition: The continuum of EM radiation categorized by wavelengths, frequencies, and energy levels.

• Three scales:

  • Wavelength in meters (m)

  • Frequency in Hertz (Hz)

  • Energy in electron volts (eV)

• All EM radiations traverse at the speed of light (c).

• No strict boundaries exist between different radiation types; spectrums overlap.

Characteristics of Radiations on the Spectrum

• Only x-rays, gamma rays, and high-energy UV rays are capable of ionization, resulting in biological damage.

• The visible light spectrum is the sole part that human eyes can detect; colors result from the separation of wavelengths.

• EM radiations interact with objects similar in size to their wavelengths.

Example EM Spectrum

• Wavelengths range from human size (10 m) to atomic scale (0.000001 nm).

  • Frequency: Ranges from 10^7 Hz up to 10^27 Hz.

  • Energy: Varies from 10^{-5} eV to 10^{4} eV.

Particle Theory

• EM radiations travel as waves, while particles (electrons, protons) possess mass and charge.

• EM radiation behavior shows wave-particle duality: it acts as a wave in some contexts and a particle in others.

• Energy and frequency of photons are directly proportional; wavelength and energy are inversely related.

Planck’s Law

• Max Planck's Contribution: Developed the equation describing energy in photons relative to frequency.

• Formula:

  • $E = h <br>u$ or $<br>u = E/h$

  • Where:

  • E = photon energy in eV

  • h = Planck's constant ($4.15 imes 10^{-15} ext{ eV-sec}$)

  • ν = photon frequency in Hz

Calculating Energy & Frequency

• Example Energy Calculation:

  • Energy of x-ray photon with frequency $2.2 imes 10^{11} ext{ Hz}$:

  • $E = hv = (4.15 imes 10^{-15}) imes (2.2 imes 10^{11}) = 9.13 imes 10^{-4} ext{ eV}$.

• Example Frequency Calculation:

  • Frequency of a 100 keV x-ray photon:

  • $v = E/h o v = (1.0 imes 10^5)/(4.15 imes 10^{-15}) o v = 2.40963855 imes 10^{20} ext{ Hz}$.

Mass-Energy Equivalence

• Concept: Matter and energy are convertible.

• Einstein’s Equation:

  • $E = mc^2$

  • Where:

    • E = energy in Joules

    • m = mass in kilograms

    • c = speed of light squared ($3.0 imes 10^8 ext{ m/s}$)

Properties of X-Rays

• Form of electromagnetic radiation capable of ionizing matter.

• Travel at light speed, are electrically neutral, and have no mass or charge.

• Cannot be seen or heard; not affected by electric/magnetic fields.

• Can be produced in various energy ranges and wavelengths.

• Cause fluorescence in crystals, produce secondary/scatter radiation, and impact matter through excitation and ionization.