The Atomic Nature of Matter, Solids, Liquids, Gases, Heat, and Sound Practice Flashcards

The Atomic Nature of Matter

• Categories of Matter: All matter can be divided into two primary categories:

  • Mixtures: The properties of a mixture change depending on the concentration of each component. Mixtures are further classified into:
    • Homogeneous: A uniform mixture throughout its volume. Examples include air, water, or lemonade.
    • Heterogeneous: A mixture that does not have uniform consistency. Examples include Italian dressing, granite, or a burrito.
  • Pure Substances: These have inherent properties such as density, melting point, etc.
    • Elements: Substances containing identical atoms.
    • Compounds: Can be composed of compounds made up of molecules. For example, water is represented as $H_2SO_4$.
  • Molecules: Consist of two or more atoms held together by atomic bonds.

• The Structure of Atoms: Atoms can be broken down into smaller components:

  • Nucleus: Contains protons and neutrons. These can be further broken down into quarks.
  • Electrons: Exist in the space surrounding the nucleus.
  • Elementary Particles: Electrons and quarks are known as elementary particles because they cannot be broken into smaller pieces.

Atomism and Early Atomic Theories

• The Nature of Matter: Humans early on questioned if matter was discrete or continuous.

  • Atomism: The philosophical idea that all matter can eventually be broken down into some type of fundamental particle.
  • Continuum: The idea that there is no fundamental particle, but rather a continuum of fluid that all matter is composed of.
    • Aristotle: Believed in the continuum model of nature. He famously stated that "Nature abhors a vacuum." He argued that if matter were made of particles, a vacuum must exist between them; however, there was no evidence to justify this philosophical argument at the time.

• Evolution of Atomic Theories:

  • Democritus (400 BCE): Proposed that everything was composed of atoms with empty space in between them. He suggested that the properties of a substance related to the properties of its constituent atoms. For example, iron atoms would be strong, water atoms would be slippery, and salt atoms would be sharp.
  • John Dalton (Early 1800s): Noted that chemical compounds consisted of whole-number ratios of proportions of elements. These specific chemical ratios are due to atomic bonds and the discrete nature of atoms (one cannot have half an atom).
  • JJ Thomson (Late 1800s): Discovered electrons through experiments with cathode-ray tubes. This showed that atoms could be broken into smaller components. He proposed the "Plum Pudding Model," knowing that atoms are electrically neutral and electrons can move around independently.
  • Ernest Rutherford (Early 1900s): Conducted the Gold Foil Experiment, shooting alpha particles (helium nuclei) at a thin piece of gold foil.
    • Most alpha particles passed through undeflected, implying most of an atom's volume is empty space.
    • Some alpha particles bounced back. Rutherford remarked: "It was almost as incredible as if you fired a 15-inch shell at a piece of tissue paper and it came back and hit you."
    • This led to the discovery of the positively charged atomic nucleus.
  • Niels Bohr (1913): Proposed that electrons orbit the nucleus in clearly defined orbits, similar to planets orbiting the sun. Each orbit was well-defined, and only certain orbits could exist based on electron energy levels. In modern understanding, electrons exist probabilistically around the nucleus.

The Periodic Table, Isotopes, and Ions

• The Periodic Table Structure:

  • Columns: Represent elements with similar chemical properties.
  • Noble Gases (Group 18): Do not react easily with other substances because they have a full shell of valence electrons.
  • Atomic Number ($Z$): Equal to the number of protons in the atom.
  • Atomic Mass: The total mass of the atom (protons and neutrons).

• Isotopes: Atoms with the same number of protons but a different number of neutrons. Many elements have naturally occurring isotopes; some are stable, while others are radioactive.

• Ions: On average, atoms are electrically neutral (number of protons = number of electrons). An excess or absence of electrons creates an electric charge. An ion is a charged atom.

  • Charge Calculation: $\text{number of protons} - \text{number of electrons} = \text{charge}$
  • Example 1: $H^-$ (Hydrogen ion). ${N}_p = 1$, ${N}_e = 2$. $\text{Charge} = -1$.
  • Example 2: $^{40}Ca^{2+}$. Atomic number is $20$, so ${N}_p = 20$. Atomic mass number is $40$, so ${N}_n = 20$. The charge is $+2$, so ${N}_e = 18$.

Antimatter and the Universe

• Antimatter: Particles with the same mass as "normal" matter but with opposite charge.

  • Proton: Mass = $1.67 \times 10^{-27} kg$, positive charge. Anti-Proton: Mass = $1.67 \times 10^{-27} kg$, negative charge.
  • Electron: Mass = $9.11 \times 10^{-31} kg$, negative charge. Positron: Mass = $9.11 \times 10^{-31} kg$, positive charge.
  • Neutron: Mass = $1.67 \times 10^{-27} kg$, zero charge. Anti-Neutron: Mass = $1.67 \times 10^{-27} kg$, zero charge.
  • Annihilation: When matter and antimatter meet, they annihilate, releasing energy according to Einstein's equation: $E = m \times c^2$.
  • Antimatter is produced naturally (radioactive decay) and artificially (particle colliders). It requires massive energy to create and exists only briefly before annihilation.

• The Standard Model and Discrepancies: The standard model accounts for only $5\%$ of our known universe. The rate of expansion of the universe cannot be explained by the amount of energy thought to exist.

  • Dark Matter and Dark Energy: Hypothesized concepts to explain these discrepancies. They do not interact with electromagnetism (light), meaning we cannot see them.

Solids

• Overview: A state of matter where atoms or molecules are tightly bound together. Solids have rigid volume and shape. They do not change shape to fit containers, nor do they change volume to take up available space.

• Structure of Solids:

  • Crystalline Solids: Atoms are arranged in an orderly, repeating fashion. The Unit Cell repeats throughout the solid. Examples: Diamonds, quartz, snowflakes. Crystalline silicon is a semiconductor used in computer chips.
  • Amorphous Solids: Atoms are arranged randomly without order. Examples: Plastics, wax, and glass.
  • Polycrystalline Solids: Characterized by short-range order but no long-range order; composed of many individual crystals. Examples: Most metals and ceramics.
  • Material Scientists: Professionals who determine properties of materials and design new ones.

• Density: Defines how compact matter is in an object.

  • Symbol: $D$
  • Equation: $D = \frac{m}{V}$
  • Units: $kg/m^3$ or $g/cm^3$.
  • Conversions: $1000 \times g/cm^3 = kg/m^3$; $(kg/m^3) / 1000 = g/cm^3$.
  • Measurement: Mass is measured with a scale. Volume for regular objects is length $\times$ width $\times$ height. For irregular objects, the Liquid Displacement Method is used. Submerge the object in water and measure the rise. A rise of $1 \text{ mL} = 1 cm^3$.

Elasticity and Forces in Solids

• Elasticity: The property of a solid object to return to its original shape after being deformed by a force.

  • Deflection: Applying force causes deflection; removing it returns the object to its original configuration.
  • Limits:
    • Yield Strength: Exceeding this causes permanent deformation (permanent stretch).
    • Ultimate Strength: Exceeding this causes the object to break.
  • Hooke’s Law: F = k \times \text{\Delta}x. Where $F$ is the applied force (N), $k$ is the spring constant/stiffness ($N/m$), and \text{\Delta}x is the distance of deflection (m).

• Spring Configurations:

  • Series Springs: Connected in one long line. The effective spring constant is smaller than a singular spring.
  • Parallel Springs: Connected side-by-side. The effective spring constant is larger than a singular spring.

• Forces: Tension and Compression.

  • Tension: Force when something is stretched or pulled apart.
  • Compression: Force when something is squeezed or pushed together.
  • Neutral Layer: A layer between tension and compression where no forces act.

Scaling

• Scaling Principles: Examines how properties change when size changes. This involves surface area, volume, and weight.
  • Surface Area: Related to the strength of a solid object.
  • Weight: Relates to volume, density, and gravitational acceleration.
  • Strength-to-Weight Ratio: Indicated by the Surface Area / Volume ratio.
    • Large Ratio: More structurally sound.
    • Small Ratio: Less structurally sound.
    • As an object scales larger (at constant density), the surface area to volume ratio decreases.

Liquids

• Properties: Molecules are free to move but still packed together. Liquids change shape but are difficult to compress (fixed volume).

• Pressure:

  • Symbol: $P$; Units: $Pa = N/m^2$ (Pascals).
  • Equations: $P = \frac{F}{A}$ or $P = D \times g \times \text{depth}$.
  • Pressure in a liquid increases as depth increases. It does not depend on the surface area or size of the body of water. Pressure 5 meters deep is the same in a pond as it is in a lake.

• Archimedes' Principle: Liquids exert an upward Buoyant Force on objects that displace them.

  • Buoyancy is caused by the difference in pressure the liquid exerts on the top vs. bottom of an object.
  • Equation: $F_B = D \times V \times g$ or $F_B = W_{\text{air}} - W_{\text{fluid}}$.
  • The buoyant force is equal to the weight of the fluid displaced.
  • Flotation: An object floats if it is less dense than the fluid; it sinks if it is more dense. A floating object displaces its own weight of fluid.

• Pascal’s Principle: A pressure change everywhere in a closed system of liquid is equal ($F_1/A_1 = F_2/A_2$).

  • This is the basis of Hydraulics, used in lifters, braking, and airplanes. Small force on a small area creates a large force on a large area.
  • Water Towers: Create pressure in water mains. All houses connected have the same pressure; if the main breaks, all lose pressure.

• Surface Phenomena:

  • Surface Tension: A force acting parallel to the surface of a liquid.
  • Capillarity: The tendency of a liquid to "climb the walls" of a container. It occurs when adhesive forces (liquid to wall) are greater than cohesive forces (liquid to liquid).

Gases and the Atmosphere

• Properties: Molecules move very freely and are arranged loosely. Shape and volume change easily. Gases can be compressed or expanded.

• The Earth’s Atmosphere: A layer of gases (approx. $80\%$ Nitrogen, $20\%$ Oxygen) providing thermal protection, UV protection, and pressure.

  • Density: Decreases with altitude. Most mass exists within $100 km$ of the surface.
  • Kármán Line: The designated start of "space."
  • Pressure: Sea level pressure is approximately $1 \text{ atm} = 100,000 Pa = 100,000 N/m^2$.
  • Barometers: Devices to measure pressure. Standard sea level is $29.92 \text{ in Hg}$. Aneroid Barometers use compressible cells.

• Gas Laws:

  • Boyle’s Law: In a closed system at constant temperature, $P \times V = \text{Constant}$. If volume decreases, pressure increases ($P_1 \times V_1 = P_2 \times V_2$).
  • Ideal Gas Law: $P \times V = n \times R \times T$. As temperature decreases, the product of $PV$ decreases.

• Buoyancy and Dynamics:

  • Gases less dense than air rise; more dense gases sink.
  • Bernoulli’s Principle: As the speed of a fluid increases, its internal pressure decreases.
  • Venturi Effect: As the area for fluid flow gets smaller, speed increases to conserve mass. Bernoulli's principle then states pressure must decrease to conserve energy. Differences in pressure on two sides of an object create a net force.

• Plasma: An ionized gas where electrons have been removed due to high energy. Found in lightning, neon lights, and auroras. Excellent for generating light.

Temperature and Heat

• Temperature ($T$): A measure of the average kinetic energy of a substance.

  • Empirical Scales: Celsius and Fahrenheit.
    • $T_F = T_C \times 1.8 + 32$
    • $T_C = (T_F - 32) \times \frac{5}{9}$
  • Absolute Scale: Kelvin ($T_K = T_C + 273$).
  • Absolute Zero: The lowest possible temperature achievable.

• Heat ($Q$): Energy transferred due to a temperature difference. Units: calories (cal) or Joules (J). Spontaneously flows only from hot to cold.

• Specific Heat Capacity ($c$): Thermal inertia; difficulty of changing a substance's temperature.

  • Equation: Q = m \times c \times \text{\Delta}T.
  • Specific heat of water is very high: $1 \text{ cal}/(g \text{ } ^\text{o}C)$.

Heat Transfer

• Conduction: Transfer via physical contact/collisions. Solids (especially metals with free electrons) are good conductors. Liquids and gases are poor conductors.
• Convection: Transfer via motion of molecules. Liquids and gases are good at this. Hot air rises due to buoyant forces.
• Radiation: Heat travels as electromagnetic light waves (Infrared). Black objects absorb more light and heat up faster. Objects heat up if they absorb more than they emit.
• Solar Power: Solar constant is $1,400 J/s/m^2$ or $1,400 W/m^2$. Used to calculate panel requirements. An average house uses $125,000 kJ$ in one day.
• Newton’s Law of Cooling: Rate of cooling is proportional to the temperature difference: \frac{\text{\Delta}T}{\text{\Delta}t} ∝ T_{\text{object}} - T_{\text{surroundings}}.

Phase Changes

• Processes:

  • Evaporation: Liquid to Gas (Energy absorbed). Cools the environment.
  • Condensation: Gas to Liquid (Energy lost). Warms the environment. Occurs at the same temperature as evaporation ($100 \text{ } ^\text{o}C$ for water).
  • Boiling: Bubbles form throughout the volume. Boiling point decreases with altitude (lower atmospheric pressure).
  • Melting/Freezing: Occur at the same temperature ($0 \text{ } ^\text{o}C$ for water).
  • Sublimation: Solid to Gas.
  • Deposition: Gas to Solid.
  • Ionization: Gas to Plasma.

• Latent Heat: Heat required for a phase change without changing temperature.

  • Latent Heat of Vaporization ($L_{HV}$): For water, it is $540 \text{ cal/g}$. Equation: $Q = m \times L_{HV}$.
  • Latent Heat of Fusion ($L_{HF}$): For water, it is $80 \text{ cal/g}$. Equation: $Q = m \times L_{HF}$.

• Triple Point: Pressure and temperature where solid, liquid, and gas coexist simultaneously.

Thermodynamics

• First Law: \text{\Delta}E = Q - W (Internal energy = Heat added - Work done).

  • Adiabatic Process: No heat is added or removed ($Q = 0$). Occurs in well-insulated systems or very quickly. If work is done on the system ($W$ is negative), internal energy increases.

• Second Law: Heat flows spontaneously from hot to cold. Natural systems tend toward increasing entropy (disorder).

  • Heat Engines: Machines using temperature differences to do work (Power plants, combustion engines, refrigerators). Efficiency is never $100\%$.
  • Carnot Efficiency: Maximum possible efficiency: $e = \frac{T_{\text{hot}} - T_{\text{cold}}}{T_{\text{hot}}}$.

• Entropy: The amount of disorder. High entropy = random arrangement. Second law states total entropy of the universe always increases.

Vibrations and Waves

• Wave Basics: Periodic oscillation transferring energy. Waves travel through space/medium; vibrations are fixed.

  • Anatomy: Crests (high points), Troughs (low points), Amplitude (max displacement), Wavelength ($\lambda$), Period ($T$), Frequency ($f$).
  • Relation: $f = 1/T$; v = \text{\lambda} \times f. Speed of sound is $340 m/s$; speed of light is $3 \times 10^8 m/s$.

• Types:

  • Longitudinal: Motion parallel to wave direction (Sound).
  • Transverse: Motion perpendicular to wave direction (Light).

• Interference:

  • Constructive: Crest to crest.
  • Destructive: Crest to trough.
  • Standing Waves: Oscillate in time but not space. Produced by interference of identical waves moving in opposite directions. Contains nodes (no move) and antinodes (move).

• Doppler Effect: Wavelength shortens (higher pitch) as source approaches; wavelength increases (lower pitch) as it moves away. Sonic Boom occurs when traveling faster than sound.

Sound and Music

• Sound Waves: Longitudinal pressure waves.

  • Frequency = Pitch; Amplitude = Volume.
  • Ultrasound: $> 20,000 Hz$. Infrasound: $< 20 Hz$.
  • Speed of Sound Equation: $v = (331 \text{ m/s}) + 0.6 \times T$
  • Beats: Interference of two similar frequencies. $f_{\text{beat}} = |f_1 - f_2|$.
  • Resonance: Object forced to vibrate at its natural frequency.

• Musical Sound:

  • Loudness: Subjective volume.
  • Intensity ($I$): Energy per area per second. $I = \frac{P}{A}$.