Comprehensive Study Guide: Atomic Structure and Energy Systems of Matter and Energy Systems

Historical Development of the Model of the Atom

• Democritus (5th Century BC): The Greek philosopher proposed that matter is composed of identical, indivisible lumps called "atomos."

• John Dalton (1804): Agreed that matter was made of tiny spheres (atoms) that could not be broken up. He suggested that each element was made of a different type of atom.

• J. J. Thomson: Discovered electrons, proving that atoms could be broken down. He proposed the Plum Pudding Model, where the atom is a sphere of positive charge with negative electrons embedded in it like fruit in a pudding.

• Ernest Rutherford (1909) - Alpha Scattering Experiment:

  • Method: Fired alpha particles at a thin sheet of gold foil. Expected particles to pass straight through or only be slightly deflected.

  • Observations:

    1. Most alpha particles passed straight through (suggesting the atom is mostly empty space).

    2. A few particles were deflected at large angles (suggesting a concentration of positive charge because like charges repel).

    3. A tiny number of particles were deflected backwards (suggesting a tiny, dense nucleus containing most of the mass).

  • Outcome: The Nuclear Model was proposed, with mass concentrated in a central nucleus.

• Niels Bohr: Refined the nuclear model by proposing that electrons orbit the nucleus at specific distances called energy levels.

• Protons: Later experiments showed the nucleus was composed of smaller particles called protons, each with a positive charge.

• James Chadwick (1932): Proved the existence of the neutron, which explained the imbalance between atomic and mass numbers.

Modern Atomic Structure and Isotopes

• Structure:

  • Nucleus: Tiny center containing protons (relative charge $+1$) and neutrons (relative charge $0$). It carries an overall positive charge and contains almost all the mass.

  • Electrons: Negatively charged (relative charge $-1$), orbiting in energy levels.

  • Atomic Neutrality: Atoms have no overall charge because the number of protons equals the number of electrons.

  • Dimensions: The radius of an atom is approximately $1 \times 10^{-10}\,m$. The nucleus is over $10,000$ times smaller than the atom.

• Energy Levels: Electrons move to a higher energy level by absorbing electromagnetic radiation and move to a lower level by releasing it. If an outer electron absorbs enough radiation, it leaves the atom, becoming a positively charged ion.

• Isotopes: atoms of the same element with the same number of protons (atomic number) but a different number of neutrons (mass number).

  • Atomic Number: Number of protons.

  • Mass Number: Total protons plus neutrons. Example: Oxygen-16 ($^{16}_{8}O$).

Nuclear Radiation and Radioactive Decay

• Radioactive Decay: Unstable isotopes decay into other elements to become more stable, releasing nuclear radiation. This process is entirely random.

• Forms of Radiation:

  • Alpha ($α$) Particles: Helium nucleus ($2$ protons, $2$ neutrons). Strongly ionizing, low range (few cm in air), stopped by paper.

  • Beta ($β$) Particles: Fast-moving electrons. Moderately ionizing, range of a few meters in air, stopped by magnesium or aluminium.

  • Gamma ($γ$) Rays: Electromagnetic waves. Weakly ionizing, long range in air, stopped by thick lead or meters of concrete.

  • Neutrons ($n$): Can be released to rebalance atomic and mass numbers.

• Nuclear Equations:

  • Golden Rule: Total atomic and mass numbers on both sides of the arrow must be equal.

  • Alpha Decay: Mass number decreases by 4, atomic number decreases by 2 ($^{238}_{92}U \rightarrow ^{234}_{90}Th + ^{4}_{2}He$).

  • Beta Decay: A neutron turns into a proton. Mass number stays same, atomic number increases by 1 ($^{14}_{6}C \rightarrow ^{14}_{7}N + ^{0}_{-1}e$).

  • Gamma Emission: No change in mass or atomic number; it is a method of releasing excess energy.

Measuring Radioactivity and Half-Life

• Terminology:

  • Activity: Rate of source decay, measured in becquerels (Bq) ($1\,Bq = 1\text{ decay/s}$).

  • Count-rate: Radiation counts measured by a detector (e.g., Geiger-Muller tube) per second (cps).

• Half-Life: The time taken for the number of radioactive nuclei in an isotope to halve, or for activity/count-rate to halve.

• Calculation Example: Initial activity is $640\,Bq$. Final activity is $160\,Bq$ after $20\text{ minutes}$.

  • $640 \rightarrow 320 \rightarrow 160$ (2 halvings). It has undergone 2 half-lives.

Energy Stores and Systems

• Energy Stores:

  1. Thermal (Internal) energy stores.

  2. Kinetic energy stores.

  3. Gravitational potential energy (GPE) stores.

  4. Elastic potential energy stores.

  5. Chemical energy stores.

  6. Magnetic energy stores.

  7. Electrostatic energy stores.

  8. Nuclear energy stores.

• Systems: A single object or group of objects. In a closed system, neither matter nor energy can enter or leave; the net change in total energy is always zero.

• Energy Transfer Methods:

  • Heating: Energy transfer to the thermal store (e.g., a kettle heating water).

  • Work Done: Energy transferred by moving particles (current) or by a force moving an object.

  • Radiation: Energy transfer by light or sound.

Calculating Energy

• Kinetic Energy ($E_k$): $E_k = \frac{1}{2}mv^2$, where $m$ is mass ($kg$) and $v$ is speed ($m/s$).

  • Example: Car of mass $2500\,kg$ at $20\,m/s$: $0.5 \times 2500 \times 20^2 = 500,000\,J$.

• Gravitational Potential Energy ($E_p$): $E_p = mgh$, where $g$ is field strength ($9.8\,N/kg$) and $h$ is height ($m$).

• Conservation for Falling Objects: When there is no air resistance, $\text{Energy lost from GPE store} = \text{Energy gained in Kinetic store}$.

• Elastic Potential Energy ($E_e$): $E_e = \frac{1}{2}ke^2$, where $k$ is spring constant ($N/m$) and $e$ is extension ($m$).

Specific Heat Capacity and Thermal Physics

• Definition: Specific heat capacity is the amount of energy needed to raise the temperature of $1\,kg$ of a substance by $1^{\circ}C$.

• Formula: $\Delta E = mcΔθ$, where $\Delta E$ is change in thermal energy ($J$), $m$ is mass ($kg$), $c$ is specific heat capacity ($J/kg^{\circ}C$), and $\Delta θ$ is temperature change ($^{\circ}C$).

• Internal Energy: The total energy stored by particles in a system, combining kinetic energy stores (due to movement/vibration) and potential energy stores (due to particle positions/bonds).

• Changes of State:

  • Heating transfers energy to kinetic stores (temperature rise) or potential stores (breaking bonds, change of state).

  • Mass is preserved during a change of state (physical change, not chemical).

Power and Efficiency

• Power ($P$): The rate of energy transfer or work done. Measured in watts (W), where $1\,W = 1\text{ joule/second}$.

  • Formula 1: $P = \frac{E}{t}$

  • Formula 2: $P = \frac{W}{t}$

• Efficiency: The proportion of energy transferred usefully.

  • $\text{Efficiency} = \frac{\text{Useful Output Energy Transfer}}{\text{Total Input Energy Transfer}}$

  • $\text{Efficiency} = \frac{\text{Useful Power Output}}{\text{Total Power Input}}$

• Waste Energy: Most devices dissipate energy as heat to the thermal energy stores of the surroundings. Lubrication reduces friction to improve efficiency.

Energy Resources

• Non-Renewable (Finite): Fossil fuels (Coal, Oil, Natural Gas) and Nuclear (Uranium/Plutonium). Reliable but cause environmental damage (global warming via $CO_2$, acid rain via sulfur dioxide, nuclear waste).

• Renewable (Infinite):

  • Wind: Turbines in exposed places. No pollution, but noisy, unsightly, and unreliable (depends on wind).

  • Solar: Cells generate electricity from light. Free energy after setup, but only works in daytime.

  • Geothermal: Energy from radioactive decay deep in Earth. Reliable and free, but limited to volcanic areas.

  • Hydro-electric: Flooding valleys with dams. Reliable and meets demand quickly, but ruins habitats and releases $CH_4/CO_2$ from rotting vegetation.

  • Waves: Coastline turbines. No pollution, but affects marine habitats and is unreliable.

  • Tides: Estuary barrages. Tides are reliable, but barrages block boats and alter habitats.

  • Bio-fuels: From plant/animal dung. Supposedly carbon neutral (if replanting happens), but expensive and requires land.

Particle Model of Matter

• Density ($\rho$): $\rho = \frac{m}{V}$, where $m$ is mass ($kg$) and $V$ is volume ($m^3$).

  • Solids: Fixed, regular arrangement; high density.

  • Liquids: Irregular, particles move past each other; slightly less dense than solids.

  • Gases: Free to move, random directions; very low density.

• Gas Pressure: Caused by particles colliding with container walls. Higher temperature increases kinetic energy, causing faster movement and more frequent/forceful collisions, thus increasing pressure.

• Experimental Density:

  • Regular Solid: Measure dimensions for volume, use a balance for mass.

  • Irregular Solid: Submerge in a eureka can; Volume of displaced water = Volume of object.