Honors Chemistry: Atomic Theory and Electromagnetic Radiation Study Notes

Atomic Structure: Subatomic Particles

Proton: location in the nucleus; charge = +1e
Neutron: location in the nucleus; charge = 0
Electron: location outside the nucleus (in orbitals/space around nucleus); charge = -1e
Subatomic particles together determine atomic properties and behavior in reactions

Key Definitions

Atomic number (Z): number of protons in the nucleus; defines the identity of the element
Mass number (A): total number of protons and neutrons in the nucleus; A = Z + N
Nucleus: dense center of the atom containing protons and neutrons (collectively called nucleons)
Atom: the basic unit of an element, consisting of a nucleus surrounded by electrons in space
Molecule: two or more atoms bound together
Isotope: atoms with the same Z but different A (different number of neutrons)
Ion: atom with a net electric charge due to loss or gain of electrons

How to Read Isotopes and Ions on the Periodic Table

Given an element, you can determine: atomic number (Z), typical mass, and electron count for neutral species
For ions, adjust electron count by the charge (e.g., Cation: fewer electrons; Anion: more electrons)
Example method (brief): for a neutral atom, electrons = protons = Z; for a cation with charge +n, electrons = Z − n; for an anion with charge −n, electrons = Z + n

Atomic Models: Historical Progression

Dalton: billiard-ball model; atoms are indivisible spheres with unique identities per element
Thomson (Plum Pudding model): discovered the electron via cathode ray experiments; atoms contain negative charges embedded in positive matrix
Rutherford (Gold Foil experiment): discovered a small, dense nucleus; atoms are mostly empty space with a central positive nucleus
Bohr: quantized orbits for electrons; energy levels determine spectral lines of hydrogen
Quantum Mechanical Model (Schrödinger): electrons occupy orbitals described by probability distributions (not fixed orbits); electron cloud concept

Thomson’s Cathode Ray Tube Experiment

Setup: gas-filled tube with voltage, producing cathode rays from the cathode to the anode
Observation: rays were deflected by electric and magnetic fields toward the positive plate, implying negatively charged particles
Particle discovered: electron
Significance: provided evidence for subatomic structure and led to the idea of charge/particle constituents of atoms

Rutherford’s Gold Foil Experiment

Setup: alpha particles shot at thin gold foil; some deflected, most passed straight through
Conclusions: atom is mostly empty space; there is a dense, positively charged nucleus; nucleus contains most of the atom’s mass
Impact: challenged the plum pudding model and established a nuclear model of the atom

Heisenberg Uncertainty Principle

Concept: there is a fundamental limit to simultaneously knowing the exact position and exact momentum of a particle
Practical form: Δx · Δp ≥ ħ/2 (where ħ = h/2π)
Implication: electrons are described by probability distributions rather than exact orbits; supports the Quantum Mechanical Model

Wave-Particle Duality of Light

Double-slit experiment: showed light exhibits interference pattern (wave-like behavior)
Photoelectric effect: showed light can eject electrons as discrete quanta (particle-like behavior)
Conclusion: light has both wave-like and particle-like properties; this wave-particle duality extends to matter as well

Average Atomic Mass (Atomic Weight)

Definition: weighted average mass of an element’s naturally occurring isotopes
Formula: ar{m} = rac{ ext{Sum of (mi × fi)}}{100} = ext{Sum}(mi × fi) where f_i is the fractional abundance (percent as a decimal)
Example calculation (given isotopic masses and abundances):
- Isotope masses (amu) and abundances: 37.910 (9.67%), 39.100 (78.68%), 40.001 (11.34%), 41.200 (0.31%)
- Fractional abundances: 0.0967, 0.7868, 0.1134, 0.0031
- Average atomic mass
  ar{m} \,= \,37.910(0.0967) + 39.100(0.7868) + 40.001(0.1134) + 41.200(0.0031) \approx 39.09 \, \text{amu}
Element identity from average mass: closest element is Potassium (K) with atomic number Z = 19

Waves and Electromagnetic Radiation: Key Concepts

Wavelength (λ): distance between successive crests of a wave; unit meters (m)
Frequency (ν): number of waves (cycles) passing a point per unit time; unit s⁻¹ or Hz
Velocity (v or c): speed of the wave; in vacuum, c = 3.00 imes 10^{8}\, \text{m/s}; relation: v = λν
Electromagnetic Spectrum: range of EM waves organized by frequency and wavelength; from longest wavelength/lowest frequency to shortest wavelength/highest frequency/highest energy
Color order in visible spectrum: ROYGBIV (Red, Orange, Yellow, Green, Blue, Indigo, Violet)

Electromagnetic Spectrum: Order and Formulas

Types of EM radiation (longest to shortest wavelength / lowest to highest frequency / lowest to highest energy):
- Radio waves → Microwaves → Infrared → Visible → Ultraviolet → X-rays → Gamma rays
Key equation: c = λν with c = 3.00 \times 10^{8}\ \text{m/s}
Planck-Einstein relations:
- Photon energy: E = hν
- Planck’s constant: h = 6.626 \times 10^{-34}\ \text{J s}
- Also useful form: E = \frac{hc}{λ}
Planck and Einstein contributions:
- Planck introduced quantization of energy (energy comes in discrete units, quanta)
- Einstein explained the photoelectric effect using photons; light as particles of energy E = hν
Fluorescence/photons: packet of energy called a photon; spectroscopy studies the interaction of light with matter to reveal electronic structure

Bohr Model and Hydrogen Emission Spectrum

Bohr proposed quantized energy levels for electrons; electrons absorb or emit energy when moving between levels
Bright line spectrum (emission spectrum) provided evidence for discrete energy levels
Practical use: spectroscopy helps identify elements and study electronic structure in chemists’ work
Flame tests: different metal ions produce characteristic flame colors due to electrons absorbing energy and rising to excited states, then returning to ground state and emitting photons at characteristic wavelengths

Energy Levels and Electron Transitions

Energy level: a fixed distance from the nucleus where electrons reside; levels correspond to specific energies
Ground state: lowest energy level
Excited state: any higher energy level than the ground state
Excitation and emission: electrons absorb energy to reach excited states; they return to lower states by emitting photons

Practice Problems and Calculations (Representative Guided Solutions)

1) A violet light with wavelength 413 nm
- a) Frequency: ν = \dfrac{c}{λ} = \dfrac{3.00\times 10^{8}}{413\times 10^{-9}} \approx 7.26\times 10^{14}\ \text{Hz}
- b) Energy per photon: E = hν = (6.626\times 10^{-34}) (7.26\times 10^{14}) \approx 4.82\times 10^{-19}\ \text{J} \approx 3.01\ \text{eV}
2) Isotope X data (X – 38, X – 39, X – 40, X – 41 with given masses and abundances)
- Most common isotope: X–39 (78.68%)
- Average atomic mass: ar{m} = 37.910(0.0967) + 39.100(0.7868) + 40.001(0.1134) + 41.200(0.0031) \approx 39.09\ \text{amu}
- Identify element X by that average mass: closest element is Potassium (K), Z = 19
3) Violet light 413 nm: frequency and photon energy (see above)

Nuclear Chemistry and Radioactivity (Nucleus, Decay, Half-Life)

5) Symbol 249Cf (Californium-249)
- a) Element: Californium (Cf)
- b) Mass number: 249
- c) Protons (Z): 98 (Californium has Z = 98)
- d) Electrons (for neutral atom): 98
- e) Neutrons: 249 − 98 = 151
6) Nuclear decay reactions
- a) Beta decay of potassium-42: ^{42}{19}K \rightarrow ^{42}{20}Ca + e^- + \bar{ν}
- b) Alpha decay of radium-226: ^{226}{88}Ra \rightarrow ^{222}{86}Rn + ^{4}_{2}He
7) Half-life from decay data: 252 days, 24.0 g → 3.0 g
- Ratio: 3.0/24.0 = 0.125 = (1/2)^{252/T{1/2}} ⇒ 252/T{1/2} = 3 ⇒ T_{1/2} = 84\ \text{days}
8) Iodine-131 with half-life 8.0 days; 4.0 g → after 40 days:
- Number of half-lives: 40/8 = 5
- Remaining: 4.0 \times (1/2)^5 = 4.0/32 = 0.125\ \text{g}
9) Carbon-14 dating: 1/4 as much C-14 as living wood
- (1/2)^n = 1/4 ⇒ n = 2 half-lives elapsed
- Age ≈ 2 × 5730 years = 11,460 years
10) Cesium-137 (t½ = 30.0 years)
- a) 16.0 g after 90 years: 90/30 = 3 half-lives ⇒ remaining 16.0 \times (1/2)^3 = 2.0\ \text{g}
- b) Time for 28.0 g to decay to 3.5 g: 3.5/28 = 0.125 = (1/2)^{t/30} ⇒ t/30 = 3 ⇒ t = 90\ \text{years}
11) Phosphorus-32 (t½ unknown) decreases from 1.2 g to 0.3 g in 28 days
- 0.3/1.2 = 0.25 = (1/2)^{28/t{1/2}} ⇒ 0.25 = (1/2)^2 ⇒ t{1/2} = 14\ \text{days}

Practice Problems: Electromagnetic Waves and Radiation (Additional Concepts)

12) EM waves from lowest to highest energy: Radio waves, Microwaves, Infrared, Visible, Ultraviolet, X-rays, Gamma rays
13) Wave-related questions based on a figure (conceptual):
- The distance from the top of one wave to the top of the next wave is the wavelength, \lambda
- Waves X, Y, Z may have the same something (depends on the figure; typically these questions explore whether they share the same wavelength or the same frequency, etc.).
- The is a measure of the number of waves that pass a point per unit time: frequency, ν
- Wave Z has a that is about five times higher than Wave Y: (depends on the figure; typically amplitude or frequency is compared; note that energy depends on frequency, not amplitude)
- Wave has the most energy and Wave has the least energy: (depends on frequency/frequency order in the figure)
- Wave has the highest frequency and Wave has the lowest frequency: (depends on the figure; highest frequency = shortest wavelength)
14) ROYGBIV stands for: Red, Orange, Yellow, Green, Blue, Indigo, Violet
15) Planck and Einstein contributions (Quantum Theory):
- Planck introduced quantization of energy; energy carried by quanta
- Einstein proposed the photoelectric effect and described light as consisting of photons with energy E = hν
16) Order of radiation by wavelength (longest to shortest): microwaves, infrared, red, green, ultraviolet
17) Bohr model statements (energy level transitions):
- a. When atoms absorb or release energy, electrons move from low to high energy levels (absorption)
- b. When atoms absorb or release energy, electrons move from high to low energy levels (emission) — this is true for emission, not absorption
18) A packet of energy in Einstein’s theory is a photon
19) As wavelength increases, frequency decreases (inverse relationship): ν = \dfrac{c}{λ}
20) As frequency increases, energy increases: E = hν
21) Does the speed of light change? In vacuum, no; in media, light speed depends on the medium
22) Wave wavelength ranges (given):
- Gamma Rays: 10^{-15} \text{ to } 10^{-11} \text{ m}
- X-rays: 10^{-11} \text{ to } 10^{-9} \text{ m}
- Ultraviolet: 10^{-9} \text{ to } 10^{-7} \text{ m}
- Visible Light: 4 \times 10^{-7} \text{ to } 7 \times 10^{-7} \text{ m}
- Infrared: 10^{-6} \text{ to } 10^{-3} \text{ m}
- Microwave: 10^{-3} \text{ to } 10^{-1} \text{ m}
- Radio waves: 10^{-1} \text{ to } 10^{5} \text{ m}
23) EM Radiation properties (circle the correct type):
- a) Higher energy: ultraviolet (UV) vs microwaves? UV
- b) Longer wavelength: blue light or infrared? Infrared
- c) Shorter wavelength: X-rays or green light? X-rays
24) Wavelengths capable of broadcasting a local radio signal: choose the one in the radio range, typically around 10^{5}\ \text{m} (the 10^5 m option)

Quick Reference: Formulas and Constants

Speed of light in vacuum: c = 3.00 \times 10^{8}\ \text{m/s}; relation: v = λν
Planck’s constant: h = 6.626 \times 10^{-34}\ \text{J s}
Photon energy: E = hν or E = \dfrac{hc}{λ}
Nuclear decay: N = N0 \left(\dfrac{1}{2}\right)^{t/T{1/2}}
Relative atomic mass (average mass): \bar{m} = \sumi mi fi where fi = \text{fractional abundance}
Bohr transitions and spectral lines underpin spectroscopy for element identification

Notes and Tips

Practice problems in this unit cover: isotopes, average atomic mass, simple nuclear decay, half-life calculations, and basic EM theory
Use the periodic table to infer Z and typical isotopic masses when solving problems about isotopes and ions
For spectral calculations, keep track of units; convert nm to meters when needed
When dealing with radioactive decay problems, identify whether the process is alpha or beta decay to write the correct nuclear equation
In flame tests, color observed corresponds to specific electron transitions in the metal ion present
In the Bohr model, remember: absorption moves electrons to higher energy levels; emission returns them to lower energy levels, emitting a photon in the process