Atomic Structure, Subatomic Particles, and Isotope Chemistry

J.J. Thomson and the Discovery of the Electron

• Cathode Ray Tube Experiments:

  • Cathode rays consist of tiny, negatively charged particles that deflect toward a positively charged plate.
  • The magnitude of deflection depends on both the charge and the mass of the particle.
  • Phosphorescent screens emit a visible fleck of light when struck by particles.
  • Because the positive particle in the tube is very heavy compared to the negative particle, deflecting it requires a significantly higher voltage to observe deflection toward the negative plate.

• Charge-to-Mass Ratios ($e/m$):

  • Cathode ray particle (electron): $-1.76 \times 10^8\,\text{Coulombs per gram}$ ($\text{C/g}$).
  • Hydrogen ion ($\text{H}^+$): $9.58 \times 10^4\,\text{Coulombs per gram}$ ($\text{C/g}$).
  • The hydrogen ion is approximately $2000$ times heavier than the cathode ray particle.
  • J.J. Thomson determined the charge-to-mass ratio for the electron, but he could not separate the two variables to determine the individual charge or individual mass.

• Key Discoveries and Significance:

  • Proved the existence of subatomic particles smaller than the atom.
  • Discovered the electron as a fundamental constituent of matter.
  • Established the numerical charge-to-mass ratio for negative particles.

• The Plum Pudding Model:

  • Replaced the solid sphere model of the atom.
  • Described the atom as a diffuse sphere of positively charged matter ("pudding" or "cookie dough") with negatively charged electrons ("raisins") embedded throughout.
  • Maintained overall atomic electrical neutrality by balancing the positive field with the negative electrons.
  • At the time of proposing this model, positive subatomic particles ($\text{H}^+$) had not yet been directly observed in cathode ray experiments.

Robert Millikan and the Oil Drop Experiment

• Experimental Context:

  • Conducted by Robert Millikan at the University of Chicago.
  • Millikan was awarded the Nobel Prize in Physics in $1923$ for this work.

• Apparatus and Design:

  • Atomizer: Used a perfume-style bulb to spray a fine mist of oil droplets into an upper chamber.
  • Telescope & Scale: Allowed direct observation of individual falling oil droplets across a built-in scale (apparatus size approximately $18\,\text{inches}$).
  • Charged Gold Plates: A top gold plate and bottom gold plate created a variable electric field ($E$) when voltage was applied.
  • X-Ray Source: Ionized gas molecules inside the chamber, causing free electrons to attach to the falling oil droplets, imparting a negative charge ($q$).

• Physics and Mathematical Equilibrium:

  • Uncharged oil droplets fall under the force of gravity ($F_g$), and their mass ($m$) is calculated from their terminal velocity:         $\text{Force of Gravity} = m \times g$
  • When an electric field ($E$) is applied across the plates, the upward electrical force ($F_e$) acts on the charged droplet:         $\text{Electric Force} = E \times q$
  • By adjusting the voltage, the downward gravitational force can be balanced exactly by the upward electrical force, suspending the oil droplet in midair:         $m \times g = E \times q$
  • Knowing mass ($m$), acceleration due to gravity ($g$), and electric field strength ($E$), Millikan calculated the total charge ($q$) on the drop.

• Experimental Results and Deductions:

  • The total charge on any oil droplet was always a whole-number integer multiple ($n$) of a fundamental charge unit:         $q = n \times (-1.60 \times 10^{-19}\,\text{Coulombs})$
  • Fundamental charge of a single electron ($e$):         $\text{Charge of Electron} = -1.60 \times 10^{-19}\,\text{Coulombs}$
  • By combining this value with J.J. Thomson's charge-to-mass ratio ($-1.76 \times 10^8\,\text{C/g}$), Millikan calculated the exact mass of an electron:         $\text{Mass of Electron} = 9.10 \times 10^{-28}\,\text{grams}$

Radioactivity and Radioactive Rays

• Discovery of X-Rays:

  • Discovered in $1895$ by Wilhelm Röntgen, who received the first Nobel Prize in Physics.
  • Produced the famous X-ray image of his wife's hand showing her finger bones and ring (she famously remarked, "I have seen my death").

• Discovery of Radioactivity:

  • Discovered in $1896$ by Henri Becquerel while investigating natural phosphorescence.
  • Stored unexposed photographic paper inside a dark drawer in a sealed envelope beneath uranium samples; the paper became fully exposed despite the lack of light.
  • Becquerel shared the $1903$ Nobel Prize in Physics with Pierre Curie and Marie Curie.
  • Marie Curie coined the term radioactivity and won a second Nobel Prize in Chemistry in $1911$ for discovering radium and polonium.

• Distinction Between Phosphorescence and Fluorescence:

  • Fluorescence: Material glows under ultraviolet (UV) illumination but stops glowing immediately once the light source is removed.
  • Phosphorescence: Material absorbs light energy, flips the spin state of excited electrons, and continues to glow over time (e.g., $15\,\text{minutes}$) as electrons slowly return to their ground state (e.g., glow-in-the-dark ceiling stars).

• Types of Radioactive Emissions (Ernst Rutherford):

  • Alpha Particles ($\alpha$): High-energy, positively charged particles with a mass $4$ times that of a hydrogen atom; identical to a helium nucleus ($^4_2\text{He}^{2+}$).
  • Beta Particles ($\beta$): High-energy, negatively charged particles with a mass approximately $\frac{1}{2000}$ of a hydrogen atom; shown to be high-speed electrons ($^0_{-1}e$).
  • Gamma Rays ($\gamma$): High-energy electromagnetic radiation possessing no mass and no electrical charge.
  • Ernst Rutherford received the Nobel Prize in Physics in $1908$ for his investigations into the disintegration of elements and the chemistry of radioactive substances at McGill University.

Ernst Rutherford and the Gold Foil Experiment

• Initial Observation (Mica Scattering):

  • Rutherford noticed that passing alpha particles through a thin sheet of mica (a mineral that easily peels into thin sheets, historically used for windows) caused photographic images to blur.
  • Without mica, the particle beam formed sharp images.
  • Inferred that mica caused small-angle scattering ($1^\circ - 2^\circ$).

• Gold Foil Apparatus and Setup ($1907$):

  • Conducted at the University of Manchester alongside Hans Geiger (inventor of the Geiger counter).
  • Alpha Particle Source: Radioactive decay of Radon-222 (radium emission).
  • Target: A thin leaf of gold metal, hammered paper-thin.
  • Detector: A phosphorescent screen inside a vacuum chamber that emitted small flashes of light (scintillations) when hit by alpha particles, viewed through a moveable telescope lens.
  • Geiger's student, Marsden (Marcin), was tasked with looking for scattering at wide angles as a control experiment.

• Experimental Observations:

  • Approximately $98\%$ of alpha particles passed straight through the foil with minimal scattering ($1^\circ - 2^\circ$).
  • Approximately $0.005\%$ of alpha particles were deflected at large angles, with some bouncing directly backward toward the source.
  • Rutherford described the result as the most incredible event of his life: "As if you fired a 15-inch shell at a piece of tissue paper and it came back and hit you."

• The Nuclear Model of the Atom:

  • The Plum Pudding model was disproved as it could not account for back-scattering of massive particles.
  • Rutherford's Interpretations:
    1. The atom is composed mostly of empty space, allowing most alpha particles to pass through unhindered.
    2. The atom contains an extremely small, dense center holding virtually all of the atom's mass (the nucleus).
    3. The dense nucleus is positively charged, causing intense electrostatic repulsion when positively charged alpha particles approach it.

• Dimensions and Subatomic Mass Scale:

  • The volume of the nucleus is approximately $\frac{1}{100,000}$ ($10^{-5}$) of the total volume of the atom.
  • The positive charge of the nucleus balances the negative charge of the surrounding electrons.
  • Electrons are dispersed throughout the empty space surrounding the nucleus.
  • Mass of a proton: $\sim 10^{-24}\,\text{grams}$ (approx. $1\,\text{atomic mass unit}$).
  • Mass of an electron: $\sim 10^{-28}\,\text{grams}$ (approx. $0.00055\,\text{atomic mass units}$).

Discovery of the Neutron and Subatomic Particle Properties

• The Beryllium Mass Discrepancy:

  • Beryllium contains $4$ protons in its nucleus, which suggested an expected mass of $4\,\text{atomic mass units}$.
  • Actual experimental mass of a beryllium atom is $9.01\,\text{atomic mass units}$.
  • Electrons (mass $0.00055\,\text{amu}$ each) could not account for the missing mass of $5\,\text{amu}$.

• Discovery of the Neutron ($1932$):

  • James Chadwick bombarded beryllium metal with alpha particles, producing a highly penetrating stream of uncharged radiation.
  • Identified the radiation as neutral subatomic particles with a mass slightly greater than that of a proton.
  • Chadwick was awarded the Nobel Prize in Physics in $1935$ and later worked on the Manhattan Project.

• Summary of Fundamental Subatomic Particles:

  • Proton:
    • Symbol: $p^+$ or $H^+$
    • Relative Charge: $+1$ (Actual Charge: $+1.60 \times 10^{-19}\,\text{Coulombs}$)
    • Mass: $\approx 1\,\text{amu}$ ($1.67 \times 10^{-24}\,\text{g}$)
  • Neutron:
    • Symbol: $n^0$ or $n$
    • Relative Charge: $0$ (Actual Charge: $0\,\text{Coulombs}$)
    • Mass: $\approx 1\,\text{amu}$ (Slightly heavier than a proton)
  • Electron:
    • Symbol: $e^-$
    • Relative Charge: $-1$ (Actual Charge: $-1.60 \times 10^{-19}\,\text{Coulombs}$)
    • Mass: $\approx 0.00055\,\text{amu}$ ($9.10 \times 10^{-28}\,\text{g}$)

• Definition of Atomic Mass Unit (amu):

  • $1\,\text{atomic mass unit}$ is defined strictly as exactly $\frac{1}{12}$ the mass of a single Carbon-12 ($^{12}\text{C}$) atom.

Atomic Number, Mass Number, and Isotopes

• Isotopes:

  • Discovered by Frederick Soddy (Nobel Prize in Chemistry in $1921$ for work on radioactive decay and isotopes).
  • Isotopes are defined as atoms of the same element containing the same number of protons but different numbers of neutrons.
  • All isotopes of an element are chemically identical and undergo identical chemical reactions.

• Atomic Symbols and Definitions:

  • Atomic Number ($Z$): The number of protons in the nucleus; uniquely defines the identity of an element.
  • Mass Number ($A$): The sum of the number of protons ($Z$) and neutrons ($N$) in the nucleus:         $A = Z + N$

• Examples of Isotopic Systems:

  • Hydrogen Isotopes:
    • Protium ($^1_1\text{H}$): $1$ proton, $0$ neutrons ($99.989\%$ natural abundance).
    • Deuterium ($^2_1\text{H}$ or $\text{D}$): $1$ proton, $1$ neutron ($0.0115\%$ natural abundance); used in deuterated solvents.
    • Tritium ($^3_1\text{H}$ or $\text{T}$): $1$ proton, $2$ neutrons (radioactive isotope).
  • Carbon Isotopes:
    • Carbon-12 ($^{12}_6\text{C}$): $6$ protons, $6$ neutrons.
    • Carbon-13 ($^{13}_6\text{C}$): $6$ protons, $7$ neutrons.
    • Carbon-14 ($^{14}_6\text{C}$): $6$ protons, $8$ neutrons.
  • Chromium-52 Notation Example ($^{52}_{24}\text{Cr}$):
    • Protons ($Z$): $24$
    • Mass Number ($A$): $52$
    • Neutrons ($N$): $52 - 24 = 28$
    • Electrons (in neutral atom): $24$

• Weighted Average Atomic Mass:

  • The atomic mass reported on the periodic table is the weighted mathematical average of all naturally occurring isotopes of an element.
  • Chlorine Case Study:
    • Naturally occurring isotopes: Chlorine-35 ($^{35}\text{Cl}$) and Chlorine-37 ($^{37}\text{Cl}$).
    • Periodic table mass: $35.45\,\text{amu}$.
    • Interpretation: Because $35.45$ is closer to $35$, Chlorine-35 is significantly more abundant (approx. $75\%$) than Chlorine-37 (approx. $25\%$).
  • No single atom has a mass of $35.45\,\text{amu}$.

Ions, Chemical Nomenclature, and Reactivity

• Ions:

  • Formed when a neutral atom or group of atoms gains or loses electrons, acquiring an overall electric charge.

• Anions:

  • Negatively charged ions formed when an atom gains electrons.
  • Named by taking the root of the element name and adding the suffix "-ide".
  • Example: A neutral chlorine atom ($\text{Cl}$) gains $1$ electron to form a chloride anion ($\text{Cl}^-$).

• Cations:

  • Positively charged ions formed when an atom loses electrons.
  • Example: A neutral sodium atom ($\text{Na}$) loses $1$ electron to form a sodium cation ($\text{Na}^+$).

• Chemical Reactivity Contrast:

  • Elemental Sodium metal ($\text{Na}$) is a soft, highly reactive metal that reacts violently with water.
  • Elemental Chlorine ($\text{Cl}_2$) is a toxic, yellow-green gas.
  • Combining sodium cations ($\text{Na}^+$) and chloride anions ($\text{Cl}^-$) produces sodium chloride ($\text{NaCl}$), non-toxic table salt safe for human ingestion.

Questions & Discussion

• Question: What was the actual physical particle that constituted the cathode ray?

  • Response: Cathode rays are composed of electrons. In a cathode ray tube, cranking up the voltage allows observation of heavy positive hydrogen ions moving in the opposite direction, but the initial cathode ray identified by J.J. Thomson was composed entirely of electrons.

• Question: Is drawing an exact diagram of the cathode ray tube required for quizzes?

  • Response: Students do not need to draw an exact schematic of a cathode ray tube. Students must understand the conceptual takeaways: the discovery of particles smaller than an atom, the presence of negative and positive charges, the electron, and the charge-to-mass ratio.

• Question: Do students need to memorize specific historical dates and Nobel Prize years?

  • Response: Dates and Nobel Prize years do not need to be memorized; they are provided to illustrate the historical context of scientific discoveries.

• Question: Must conversion constants, such as charge in Coulombs or Avogadro's number, be memorized?

  • Response: Specific constants such as the unit of charge in Coulombs ($1.60 \times 10^{-19}\,\text{C}$) and Avogadro's number will be provided on assessments.

• Question: Does any single atom match the exact decimal mass listed on the periodic table?

  • Response: No single atom has a mass equal to the decimal mass on the periodic table. Values like $35.45\,\text{amu}$ for chlorine or $12.011\,\text{amu}$ for carbon represent weighted mathematical averages of all naturally occurring isotopes of that element.