Structure of Atom: Subatomic Particles

Introduction to the Mind Map Series and Structure of Atom Chapter

• The Mind Map series helps students quickly revise chapters for exams.
• Designed for students already familiar with the material.
• The Structure of Atom chapter is expected to have a minimum of two questions in exams.
• The chapter is divided into four sections: discovery of subatomic particles, atomic models, quantum mechanical model (including spectra, de Broglie, Heisenberg principle), and quantum numbers.

Discovery of Subatomic Particles: Electron

• Focuses on the historical context and experiments leading to the electron's identification.
• Cathode Ray Experiment:
  • J.J. Thomson conducted the experiment using a perforated anode.
  • Crookes observed that air becomes conductive at low pressure under high voltage, which preceded Thomson's work.
• Setup and Observations:
  • A discharge tube was used with a cathode and a perforated anode.
  • A fluorescent screen (ZnS) was placed behind the anode to detect radiation.
  • At very low pressure and high voltage, radiation was observed originating from the cathode side.
• Properties of Cathode Rays:
  • Travel in straight lines.
  • Composed of negatively charged particles initially called "negatrons" by Thomson (later named electrons).
  • Exhibit heating and mechanical effects.
  • The e/m ratio is independent of the gas and cathode material used.
• Thomson's e/m Experiment
  • Thomson modified the cathode ray tube.
  • He applied electric and magnetic fields to observe the deflection of cathode rays.
  • Cathode ray deviation depends on charge and electric/magnetic field strength.
  • Deviation is inversely proportional to mass.
  • Thomson successfully determined the e/m ratio for electrons.
• Millikan's Oil Drop Experiment and Charge Determination
  • Robert Millikan determined the charge on an electron.
  • Balanced gravitational, drag force, and electrostatic forces to suspend charged oil droplets.
  • Determined the elementary charge.
  • Charge of an electron: 1.6 x 10^-19 Coulombs.
  • Mass of an electron: 9.1 x 10^-31 kg.
  • The e/m ratio for an electron: 1.75 x 10^11 C/kg.
  • All charges in nature are integral multiples of this elementary charge (quantization).

Discovery of Subatomic Particles: Proton and Neutron

• Proton Discovery:
  • The anode ray experiment with a perforated cathode was used to discover protons.
• Experimental Setup:
  • Similar to the cathode ray experiment, but with a perforated cathode.
  • High voltage is applied.
  • Gases ionize at very low pressure.
  • Electrons move towards the cathode, and positive charges move towards the anode.
• Properties of Anode Rays:
  • Anode rays are also known as canal rays.
  • They are invisible.
  • Travel in straight lines.
  • Consist of positively charged particles.
  • The e/m ratio depends on the nature of the gas.
  • The e/m ratio is maximum for hydrogen gas.
• Neutron Discovery:
  • Discovered by James Chadwick.
  • Beryllium was bombarded with alpha particles to produce neutrons.
• Specific Charge Comparison:
  • The e/m ratio is highest for electrons, followed by protons.
  • Neutrons have no charge, resulting in a zero e/m ratio.

Atomic Models

• Thomson's Model:
  • Proposed that the atom is a positive sphere with electrons embedded in it.
  • Atoms are positive spheres.
  • Electrons are embedded.
  • Explained the neutrality of the atom.
  • Estimated the radius of the atom to be around 10^-10 meters.
• X-ray Discovery and Radioactivity:
  • Cathode rays striking heavy metals generate X-rays (discovered by Roentgen).
  • X-rays led to increased interest in radioactivity.
  • Radioactivity: spontaneous disintegration of elements like thorium and uranium.
    • Alpha rays = Helium nuclei (He+2).
      • e/m alpha = 1/2 x e/m proton.
    • Beta rays = Electrons with high specific charge.
      • Cause maximum effect on photographic plates.
    • Gamma rays = No charge, but very harmful.
• Rutherford's Model:
  • Gold foil experiment using alpha particles.
  • Three observations:
    • Most alpha particles passed undeflected.
    • Some deflected slightly.
    • Very few bounced back.
• Conclusions of Rutherford's Model:
  • Most of the atom is empty space.
  • Electrons revolve around a central nucleus.
  • Most of the alpha particles pass through without deflection.
  • Some particles are deflected at small angles.
  • Very few alpha particles get reflected directly back.
    • The tiny nucleus is positively charged.
• Key Concepts from Rutherford's Experiment:
  • Distance of closest approach: the distance at which an alpha particle's kinetic energy is converted to potential energy as it approaches the nucleus.
    • Directly proportional to the atomic number (Z).
    • Inversely proportional to kinetic energy or the square of velocity.
  • The radius of the nucleus is around 10^-15 meters.
  • The volume of the atom is 10^15 times the volume of the nucleus.
• Forces in Rutherford's Model:
  • Electrostatic force balances the centrifugal force to keep electrons in orbit.
• Drawbacks of Rutherford's Model:
  • Maxwell's Objection:
    • According to Maxwell, accelerated charged particles emit radiation.
    • Electrons should lose energy and spiral into the nucleus in approximately 10^-8 seconds, which does not happen.
  • Inability to explain discontinuous hydrogen spectra.

Electromagnetics and Quantum Theory

• Electromagnetic Radiation
  • Waves with wavelength, frequency, and velocity.
  • Velocity = Wavelength * Frequency.
  • The velocity of EM waves equals the speed of light (c = 3 x 10^8 m/s).
  • Frequency and wavelength are inversely proportional.
  • Wave number is the reciprocal of wavelength (1/λ).
  • Time period is the inverse of frequency.
• Electromagnetic Spectrum
  • Radio, Microwave, Infrared, Visible, UV, X-ray, Gamma, Cosmic.
  • Frequency increases from Radio to Cosmic.
  • Wavelength decreases from Radio to Cosmic.
• Planck's Quantum Theory:
  • Radiation is discontinuous and consists of small energy packets called quanta or photons.
  • Energy is directly proportional to frequency: E = hν.
  • h (Planck's constant) = 6.626 x 10^-34 Js.
  • Relation: E = hc/λ.
  • Values to Remember: hc = 1240 eV nm.
  • Energy and frequency are directly proportional.
  • Energy and wavelength are inversely proportional.
  • Total energy for n photons: E = n * hν.
  • Power is energy per unit time (unit: Watt).
  • Frequency and Wavelength Additivity:
    • Frequencies are additive.
    • 1/λ_absorbed = 1/λ_emitted1 + 1/λ_emitted2.
    • Wave numbers: v_absorbed = v_emitted1 + v_emitted2.
• Electron Volt (eV):
  • Unit used to express energy.
  • 1 eV = 1.6 x 10^-19 Joules.
  • Quick Calculation: λ (in nm) = 1240 / Energy (in eV).

Photoelectric Effect

• Hertz's Experiment:
  • Electrons are emitted from a metallic surface when a suitable frequency of light is incident on it.
• Einstein's Explanation:
  • Incident energy is used to overcome the threshold energy (work function) and provide kinetic energy to the emitted electrons.
  • Photoelectric effect occurs only if:
    • Incident energy > Threshold energy
    • Incident frequency > Threshold frequency
    • Incident wavelength < Threshold wavelength
• Einstein's Formula:
  • Incident energy = Threshold energy + Kinetic energy
  • hν = hν_0 + KE
  • KE = hν - hν_0
  • KE = hc (λ - λ_0) / (λ * λ_0)
• Implications of Intensity
  • Increasing the intensity increases the number of photoelectrons.
  • Intensity has no effect on kinetic energy.
• Stopping Potential:
  • Stoppping Potential = Kinetic Energy/ Charge on Electron.
• Work Function Graphical Representation:
  • Kinetic Energy = hν (Freequency) - h ν (_0) (Threshold)

Bohr's Model

• Applicability:
  • Valid only for one-electron systems (e.g., H atom, He+, Li2+).
• Postulates:
  • The electrostatic force of attraction between the nucleus and electron equals the centrifugal force.
  • Angular Momentum Quantization:
    • Angular momentum (mvr) is an integral multiple of h/2π.
    • mvr = n * h / (2π)
  • Electron energy is determined by the orbit.
  • Electrons lose or gain energy only when they transition between orbits.
• Radius of nth Orbit:
  • r_n = 0.529 * n^2 / Z Å (angstroms)
  • r_n = 52.9 * n^2 / Z pm (picometers)
  • Relative radii: r1/r2 = (n1^2/n2^2) * (Z2/Z1).
• Velocity of Electron in nth Orbit
  • 2.18 * 10^6 (z/n) (m/s)
• Comparisons of Velocity
  • Inversely proportional to n2/n1.
• Circumference
  • C = 2πr
  • C is directly Proportional to the Radius of the nth Orbit
• Time Period:
  • Time Period = Distance (Circumference/ Velocity).
• Energy of nth Orbit:
  • E_n = -13.6 * Z^2 / n^2 eV
  • E_n = -2.18 x 10^-18 * Z^2 / n^2 Joules/atom.
  • Potential energy = -kZe^2/r.
  • Kinetic energy = kZe^2/2r.
  • Total energy = -kZe^2/2r.
  • T.E. = -K.E. = 1/2 P.E.
• Effects of increasing Orbit:
  • Radius increases.
  • Velocity decreases.
  • Energy increases (becomes less negative).
  • Energy Gap Decreases
• Ionization Energy:
  • Ionization energy is the energy required to remove an electron from the atom completely.
  • Reverse the Sign of the Original Energy Equation
• Hydrogen Atom Energy Levels:
  • Calculate Electron Voltages based on Electron Placement: E1= -13.6 eV, E2= -3.4 eV, E3= -1.51 eV, Etc. Electronic transitions between lower to higher levels = Energy absorption Electronic transitions between Higher to lower levels = Energy Emission
  • Lower to Higher = Absorption Spectra
  • Higher to Lower = Emission Spectra

Hydrogen Spectra

• Spectral Series Definition:
  • When an electron transitions between energy levels, it emits energy in the form of light.
  • Transitioning from higher n2 to lower n1 levels = Rediations
  • Total Lines Emitted: n_2 - n_1 (n_2 +n_1 +1 /2)
• Types of Series:
  • Lyman series: n1 = 1 from (ultraviolet radiation).
  • Balmer series: n1 = 2 (visible region).
  • Paschen series: n1 = 3 (infrared).
  • Brackett series: n1 = 4 (infrared).
  • Pfund series: n1 = 5 (infrared).
• Series Mapping Key Points to Understand and Remember:
  • Lymer = Direct Jump to One from Any Value = UV Series
  • Balmer = Direct Jump to 2 from Any Value = VIsble Series
  • Paschen = Direct Jump to 3 from Any Value = Infrared
  • Brackett = Direct Jump to 4 from Any Value = Infrared
  • PFund = Direct Jump to 5 from Any Value = Infrared
• Energy Relationships: Alpha (first line): Smallest Gap - Minimal Energy , Max Wavelength Beta (2nd Line) = 1 number After Alpha Gamma (3rd Line) = 2 numbers After Alpha
• Formula for Wavelength
  • 1/ λ = RH = 1/ N1 ^2- 1/ N2^2
  • The Wavelength is used for Redberg's Constant - 1.097 X 10^7.
  • Use 1/ r = 912 Angstrom for ease.

Limitations of the Atomic Models

• Bohr's Failures
  • Could Not Account for Zeeman and Stark Effects
  • Zeeman : Spectra Splitting While Mag Field Present
  • Stark : Spectra Splitting While Elect Field Present
  • Not Valid for multi - electron systems.
  • The Reason that MVR = NH/2 PI is not good enough

Quantum Mechanics Models and Theories

• De Brogile Theories:
  • Any moving particle has wave - like traits.
  • Wavelength = Inversely Proportional to Momentum.
  • λ = h/p = h/mv
  • = h/ 2 mass * KE
  • = h/ Underroot 2 charge StopPot

De Broglie's Work with Bohr's Model

• De Broglie shows that circumference = N wave length in relation.
• MVr + N h/ 2 PI

Heisenberg's Work : The Uncertainty Principle

• It is not possible to determine the perfect positioning and motion of electrons.
• Delta X * Delta P greater than / equal to h/4 Pie
• Where delta X = Uncertainty of position and delta p = uncertainty of momentum.

The Schrodinger Equations

• (Del^2) Psi + BPI^2 m/ h^2 (e-v) PSI = 0
• H PSI = E PSI, where h = Hamiltonian Opp.
• The Solutions the Schrodinger equation are what we need and there are 3 : NLM set.
• Numbers are : Principal, Asymuthal, and Magentic Numbers Respectively.
  • N = 1 -> infinity
  • L = 0 -> N- 1
  • M = -L to +L with zero.
• Quantum Numbers - Numbers that give the exact identity and location of electrons in atom by defining: Shape, orientation and energy.

Quantum Numbers Explained

• Principal Quantum Numbers (N) = Orbit, can get Radius and Energy of orbit.
• Azimuthal = Shape and Number of Subshells ( L ) values - 0 to N- 1. where l subshells = s, P D f. Angular Momentusm for Subshell - Underroot (L+l+1 h/2 pi)
• Magnetic number m helps orient electrons in subshells : value comes from - L to Zero to +L orientation. S = 1 orbital set P = 3 orbital set ( pz, px, py,) D Five Orbital Set.
• Spins (s) = 1 / 2 , -1/ 2.
• Given N - number of subshells = N. Number of orbitals = N- square.
• Give L - Number orbitals + 2 (L+ 1) Max number = 4L+2

Rules of Applications for Quantum Numbers

• Apply Orbital Principles - The Lower Energy is always filled first - N+l rules - where. Whichever is highest = Highest Energy. If two are equal, then higher N has the higher Energy.
• Filling order is like SO SO poof.. Use the shortened methods to remember. Inert gases can also easily be found.
• Hunds Rule Says Pairings can only be made after orbital all have 1 unpaired electron.
• Pauli Exclusion Principle = No number of electrons two have same values Spin is then arranged using the two principles.
• Shapes -S is ALWAYS spherical -P is dumb bell shaped.
  • D is always dual dumb bell shaped.
• Key Points - Check for regions or areas where the probability of finding an electron is Zero, these are :
• Radial Nodes : value - N-L-1
• Angular Nodes: Values = l (for 3z case, no node) check where xy or xyz can't exist.
• Magnetic Rules also apply. Where para - (One Unpaired), Momentum = Underroot n+n+2. Die - fully paired