Models of the Atom Review

Models of the Atom

MoA.1: Experimental Evidence and Modern Atomic Models

Cathode Ray Tube Experiment:
- Demonstrated that a beam of light comprises charged particles, which are 1000 times smaller than a hydrogen atom.
- Change to Atomic Model: Showed that atoms are not indivisible and contain smaller, negatively charged particles (electrons).
Gold Foil Experiment:
- Positively charged alpha particles were directed at a thin gold foil.
- Most particles passed through undeflected, but some were deflected or bounced back.
- Change to Atomic Model: Indicated that an atom has a small, dense, positively charged nucleus surrounded by mostly empty space.
Line Spectra of Energized Atoms:
- Each element emits a unique color and line spectrum when energized.
- Change to Atomic Model: Suggested that electrons exist in specific energy levels and emit energy (light) when transitioning between these levels.

MoA.2: Atomic Structure and Calculations

Atomic Number:
- Identifies an atom of a specific element.
Isotopes:
- Atoms of the same element with the same number of protons but different numbers of neutrons.
- Example: Silicon-28, Silicon-29, and Silicon-30.
- Same: number of protons.
- Different: number of neutrons, mass number.
Isotope Notation and Calculations
- The mass number is the sum of protons and neutrons in the nucleus.
- Isotope Symbol: $^{A}_{Z}X$ , where:
  - $X$ = element symbol
  - $Z$ = atomic number (number of protons)
  - $A$ = mass number (number of protons + neutrons)
Ions:
- Atoms that have gained or lost electrons, resulting in a net charge.
- Cations: positively charged ions (loss of electrons).
- Anions: negatively charged ions (gain of electrons).
Average Atomic Mass Calculation:
- Weighted average of the masses of all isotopes of an element.
- Formula: $Average \ Atomic \ Mass = \sum (Isotope \ Mass \times Relative \ Abundance)$
  Example Calculations:
Radioactive Decay Equations:
- Beta+ Decay (Positron Emission): A proton in the nucleaus is converted into a neutron, releasing a positron ( $e^+$
 - Generic Equation: $^{A}{Z}X \rightarrow \ ^{A}{Z-1}Y + \ ^{0}_{+1}e$
 - Example: Cobalt-54:
 - $^{54}{27}Co \rightarrow \ ^{54}{26}Fe + \ ^{0}_{+1}e$
- Beta- Decay: A neutron in the nucleus is converted into a proton, releasing an electron ( $e^-$
 - Generic Equation: $^{A}{Z}X \rightarrow \ ^{A}{Z+1}Y + \ ^{0}_{-1}e$
 - Example: Zinc-71:
 - $^{71}{30}Zn \rightarrow \ ^{71}{31}Ga + \ ^{0}_{-1}e$
- Alpha Decay: Emission of an alpha particle ( $\alpha$ , which is a helium nucleus, $^4_2He$ ) from the nucleus.
 - Generic Equation: $^{A}{Z}X \rightarrow \ ^{A-4}{Z-2}Y + \ ^{4}_{2}He$
 - Example: Uranium-238:
 - $^{238}{92}U \rightarrow \ ^{234}{90}Th + \ ^{4}_{2}He$
Half-Life:
- The time required for half of the radioactive atoms in a sample to decay.
- After $n$ half-lives, the remaining amount is $\frac{1}{2^n}$ of the original amount.
- Example: If a sample of 1,000 radioactive atoms has a half-life of 15 hours, to find how much time will pass until only 62 atoms remain:
- $1000 \xrightarrow{1} 500 \xrightarrow{2} 250 \xrightarrow{3} 125 \xrightarrow{4} 62.5$
- It takes 4 half-lives, so $4 \times 15 = 60$ hours

MoA.3: Electron Configuration and Orbital Diagrams

Maximum Number of Electrons in Sublevels:
- s sublevel: 2 electrons
- p sublevel: 6 electrons
- d sublevel: 10 electrons
- f sublevel: 14 electrons
Maximum Number of Electrons in Energy Levels:
- Energy level $n$ can hold $2n^2$ electrons.
- For example, the 5th energy level can hold $2(5^2) = 50$ electrons; however, only 32 electrons are typically accommodated due to sublevel restrictions.
Number of Orbitals in Sublevels:
- s sublevel: 1 orbital
- p sublevel: 3 orbitals
- d sublevel: 5 orbitals
- f sublevel: 7 orbitals
Comparing Energy of Sublevels:
- Use the Aufbau principle and the $n + l$ rule to determine the order in which electrons fill sublevels.
- Electrons first fill the orbitals with the lowest energy.
- If two sublevels have the same $n + l$ value, the sublevel with the lower $n$ value is filled first.
Orbital Diagrams:
- Use boxes to represent orbitals and arrows to represent electrons.
- Follow Hund's rule: within a sublevel, electrons are individually placed into each orbital before any orbital is doubly occupied.
Electron Configurations:
- Shorthand notation showing the number of electrons in each sublevel.
- Example: Iodine (I): $1s^22s^22p^63s^23p^64s^23d^{10}4p^65s^24d^{10}5p^5$
- Valence electrons are those in the highest occupied energy level.
Electron Configurations of Ions:
- Anions (negative ions): add electrons to the electron configuration.
  - Example: I-: $1s^22s^22p^63s^23p^64s^23d^{10}4p^65s^24d^{10}5p^6$
- Cations (positive ions): remove electrons from the electron configuration, starting with the outermost energy level.
  - Example: Ti2+: 1s^22s^22p^63s^23p^64s^23d^2
    \rightarrow 1s^22s^22p^63s^23p^63d^2

MoA.4: Periodic Trends

Families/Groups:
- Alkali Metals (Group 1):
  - Ending electron configuration: $ns^1$
  - Ion charge: +1
  - Number of valence electrons: 1
- Alkaline Earth Metals (Group 2):
  - Ending electron configuration: $ns^2$
  - Ion charge: +2
  - Number of valence electrons: 2
- Transition Metals (Groups 3-12):
  - Variable oxidation states.
- Halogens (Group 17):
  - Ending electron configuration: $ns^2np^5$
  - Ion charge: -1
  - Number of valence electrons: 7
- Noble Gases (Group 18):
  - Ending electron configuration: $ns^2np^6$ (except Helium, which is $1s^2$ )
  - Inert (unreactive)
Atomic Radius:
- The distance from the nucleus to the outermost electron.
- Trends:
  - Decreases across a period (left to right) due to increasing nuclear charge (more protons).
  - Increases down a group due to the addition of energy levels.
- Example: Sodium (Na) vs. Magnesium (Mg):
  - Na has a larger radius because it has fewer protons than Mg, resulting in less attraction between the nucleus and electrons.
Electronegativity:
- The ability of an atom to attract electrons in a chemical bond.
- Trends:
  - Increases across a period (left to right) due to increasing nuclear charge.
  - Decreases down a group due to increasing atomic radius (valence electrons are farther from the nucleus).
- Example: Carbon (C) vs. Oxygen (O):
  - C has a lower electronegativity because it has fewer protons than O, resulting in less attraction for electrons.
Ionization Energy:
- The energy required to remove an electron from an atom.
- Trends:
 - Increases across a period (left to right) due to increasing nuclear charge and decreasing atomic radius.
 - Decreases down a group due to increasing atomic radius (valence electrons are farther from the nucleus).
- Example: Chlorine (Cl) vs. Bromine (Br):
 - Cl has a larger first ionization energy because its valence electrons are closer to the nucleus than Br's valence electrons.
 *Ranking Example: Ionization Energy:
- Boron (B), Carbon (C), Nitrogen (N): N > C > B (highest to lowest)
 *Ranking Example: Atomic Radius:
- Boron (B), Aluminum (Al), Gallium (Ga): B < Al < Ga (lowest to highest)