Atomic Structure, Subatomic Particles, and the Historical Development of the Periodic Table

Cathode Ray Tube Experiments and the Discovery of the Electron

• Experimental Apparatus and Setup:

  • The cathode ray tube (referred to in lecture as the Calvin brain tube experiment) consists of a sealed glass tube placed under a high vacuum where virtually all air has been pumped out.
  • The source of the ray is a metallic cathode made of metals such as platinum.
  • Energizing the cathode with electricity causes it to emit a visible beam of light/rays (represented schematically as a green line).

• Testing Behavior in Electric Fields:

  • To determine if the beam was simple light or composed of charged matter, the beam was directed between two electrically charged parallel plates (one upper plate and one lower plate).
  • Light is unaffected by electric fields and would pass straight through without deflection.
  • When voltage was applied with a positively charged upper plate and a negatively charged lower plate, the beam deflected away from the negative plate and toward the positive plate.
  • To rule out gravitational pull, the polarity was reversed (making the bottom plate negatively charged and the top plate positively charged). The beam consistently deflected away from the negatively charged plate.

• Deduction of the "Corpuscle":

  • Because like charges repel and opposite charges attract, deflection away from the negative plate proved that the beam carried a negative electrical charge.
  • J.J. Thomson hypothesized that the beam was a stream of negatively charged subatomic particles, which he termed "corpuscles" (a dictionary term meaning an extremely tiny particle).

• Implications for Atomic Structure:

  • The negatively charged corpuscles originated directly from the metal atoms composing the cathode.
  • Prior scientific consensus held that atoms were indivisible particles. The extraction of smaller negative particles proved that atoms are divisible.
  • Since intact atoms are electrically neutral, the removal of negative charge implied the existence of a corresponding positive charge remaining within the atom.

Determining the Charge-to-Mass Ratio ($\frac{e}{m}$) of the Electron

• Calculation of the Ratio:

  • By measuring the magnitude of beam deflection against the applied electric field strength, Thomson calculated the charge-to-mass ratio ($\frac{e}{m}$) for corpuscles.
  • The measured charge-to-mass ratio was on the order of $10^{11}\,\text{C/kg}$.

• Comparison with the Proton:

  • The charge-to-mass ratio of a hydrogen ion ($\text{H}^+$ / proton) was known to be on the order of $10^7$ to $10^8\,\text{C/kg}$ (specifically measured near $9.8 \times 10^7\,\text{C/kg}$ to $9.8 \times 10^8\,\text{C/kg}$).
  • Thomson's ratio for corpuscles was roughly $4$ orders of magnitude ($10,000$ times) larger than that of the lightest known atomic ion.

• Interpretation of the Large Ratio:

  • A very large ratio $\frac{e}{m}$ mathematically requires either an enormous numerator ($e$) or an extremely small denominator ($m$).
  • Thomson reasoned that because measured ionic charges across various chemical elements were known to be similar in magnitude, the charge $e$ on the corpuscle should be comparable to known charges.
  • Consequently, he concluded that the mass $m$ must be exceptionally small—calculating that corpuscles were approximately $1,800$ times smaller in mass than a hydrogen atom.

• The Plum Pudding Model:

  • Thomson proposed the "plum pudding model" to account for atomic structure based on these discoveries.
  • The atom was envisioned as a uniform sphere of positive charge (the "pudding") with tiny negatively charged corpuscles (the "plums") evenly distributed throughout.
  • In this model, the corpuscles were considered so small that they contributed negligible mass to the overall atom.

Millikan's Oil Drop Experiment and Charge Quantization

• Purpose of the Experiment:

  • Robert A. Millikan designed the oil drop experiment to determine the absolute charge ($e$) of an individual electron.
  • Determining $e$ allowed the exact mass ($m$) of the electron to be calculated algebraically using Thomson's charge-to-mass ratio:   $m = \frac{e}{\left(\frac{e}{m}\right)}$

• Apparatus and Experimental Procedure:

  • A nozzle/atomizer sprayed a fine mist of nebulized oil droplets into an upper chamber.
  • Droplets fell under gravity through a minute pinhole into a lower viewing chamber.
  • Millikan and his graduate students observed individual falling droplets through a magnified microscope lens to measure their falling speed.
  • An electric field of variable voltage was applied across plates in the chamber to exert an upward electrostatic force on the charged droplets.
  • Adjusting the voltage enabled researchers to slow down droplets, suspend them motionlessly in mid-air (balancing gravity with electrostatic repulsion), or drive them upward.

• Findings and Numerical Accuracy:

  • Millikan demonstrated that negative charge on droplets always occurred in discrete integer multiples of a single fundamental constant, proving that charge is quantized.
  • In his 1913 paper published during World War I, Millikan reported the charge of an electron as $1.5 \times 10^{-12}\,\text{C}$ (referenced alongside $1.59 \times 10^{-19}\,\text{C}$).
  • The currently accepted modern value is $1.60 \times 10^{-19}\,\text{C}$. Millikan's original measurement differed by less than $1\%$ from modern values.
  • Millikan was awarded the Nobel Prize in Physics for this groundbreaking achievement.

• Data Manipulation and Impact on Scientific Progress:

  • Examination of Millikan's personal laboratory notebooks after his death revealed that he selectively published data, discarding observations that did not fit his target value.
  • Because Millikan was an influential, highly decorated scientist, subsequent researchers attempting to replicate his experiment assumed their own apparatuses were faulty when they measured higher values.
  • Other scientists admitted to discarding their own "outlier" data or adjusting results to fit Millikan's published figure before publishing.
  • This loss of scientific and academic integrity caused published values in scientific literature to creep up slowly over many years rather than correcting immediately, delaying global scientific progress.

Rutherford's Gold Foil Experiment and the Nuclear Model

• Experimental Setup:

  • Ernest Rutherford, a physicist from New Zealand, set out to test Thomson's plum pudding model in the late 1800s / early 1900s.
  • Alpha particle source: Radioactive material placed inside a protective lead/iron block emitted a focused beam of alpha particles.
  • Alpha particles ($\alpha$) are helium nuclei ($\text{He}^{2+}$), consisting of $2$ protons and $2$ neutrons with both electrons removed (the second lightest atom after hydrogen).
  • Target: A sheet of gold hammered extremely thin and flat.

• Expected vs. Observed Results:

  • Expected: If mass and charge were evenly distributed as described by the plum pudding model, heavy alpha particles would pass straight through the foil with zero or negligible deflection.
  • Observed: Most alpha particles passed directly through without deflection, but approximately $1$ in every $20,000$ particles deflected at severe angles or bounced straight back toward the source.
  • Rutherford described the shock using the metaphor: "It was as if you fired a 15-inch shell [artillery shell] at a piece of tissue paper and it came flying back at you."

• Conclusions Regarding the Atom:

  • Severe deflections proved that alpha particles were striking an extremely dense, concentrated positive mass inside the atom, which Rutherford named the nucleus.
  • Because $19,999$ out of $20,000$ alpha particles passed completely unobstructed, Rutherford concluded that an atom consists almost entirely of empty space.

• Scale Thought Experiment:

  • Imagine scaling up an atom such that its central nucleus becomes the size of a standard basketball held in a classroom.
  • The outer boundary of the surrounding electron cloud would extend past the room, past the university campus, past a local naval base ($0.5$ to $1\,\text{mile}$ away), crossing the bay all the way to Portland.
  • Almost all atomic mass is concentrated in the central basketball-sized nucleus, while the enormous volume surrounding it up to miles away contains only vast empty space and light electrons.

Standard Atomic Notation and Subatomic Particles

• Atomic Notation Rules:

  • Standard atomic notation is written as ${}_Z^A \text{E}$:
  • $\text{E}$: The elemental symbol (e.g., $\text{H}$ for hydrogen, $\text{He}$ for helium, $\text{C}$ for carbon).
  • $Z$: The atomic number, an integer representing the exact number of protons in the nucleus.
  • $A$: The mass number, an integer representing the total sum of protons plus neutrons ($A = \text{protons} + \text{neutrons}$).

• Definition of an Element:

  • A chemical element is strictly defined by its number of protons ($Z$).
  • Any atom containing exactly $6$ protons is Carbon ($\text{C}$), regardless of the number of neutrons or electrons it possesses.

• Isotope Analysis Example (${}_2^4 \text{He}$):

  • Elemental symbol $\text{E} = \text{He}$ (Helium).
  • Atomic number $Z = 2$ ($2$ protons).
  • Mass number $A = 4$ ($4$ total nucleons).
  • Number of neutrons = $A - Z = 4 - 2 = 2\,\text{neutrons}$.

• Discovery of the Neutron:

  • James Chadwick, a graduate student/colleague connected to Millikan's academic circle, discovered the neutron.
  • Protons ($+$) and electrons ($-$) were easily discovered because their electric charges interact with magnetic and electric fields.
  • Neutrons carry neutral charge ($0$ charge) and are completely unaffected by magnetic or electric fields, making them far more difficult to detect experimentally.

Historical Development of the Periodic Table

• Mid-19th Century Background:

  • By the mid-1800s, chemists had identified approximately $60$ distinct elements (about half of the $118$ elements on the modern periodic table).
  • At the time, elements were viewed as a collection of disconnected facts, with no recognized underlying framework or logic organizing them.

• Döbereiner's Triads (Johann Wolfgang Döbereiner):

  • Grouped elements into triads (groups of three) based on similar chemical behavior and quantitative weight relationships.
  • Alkali Metal Triad: Lithium ($\text{Li}$), Sodium ($\text{Na}$), and Potassium ($\text{K}$).
  • Predicted that the middle element (Sodium) possessed an atomic mass equal to the average of Lithium and Potassium ($23.2\,\text{amu}$ predicted vs $23.1\,\text{amu}$ actual).
  • All three metals share similar chemical behavior, reacting violently/explosively with water (e.g., pure metallic sodium stored in oil explodes when dropped into water/toilets).
  • Halogen Triad: Chlorine ($\text{Cl}$), Bromine ($\text{Br}$), and Iodine ($\text{I}$).
  • Averaging Chlorine and Iodine yielded a predicted mass for Bromine of $78.4\,\text{amu}$ (actual value $81\,\text{amu}$).

• Newlands' Law of Octaves (John Newlands, 1865):

  • Arranged elements in order of increasing atomic mass.
  • Observed that chemical properties repeated every $8^\text{th}$ element, drawing an analogy to the $8$ notes in a musical octave.
  • Limitation: The Law of Octaves functioned well for light elements but broke down completely past Calcium ($\text{Ca}$), failing for heavier elements like Rubidium ($\text{Rb}$).

• Mendeleev's Periodic Law (Dmitri Mendeleev):

  • Recognized as the father of the modern periodic table.
  • Originally ordered elements by atomic mass like his predecessors, but realized strict mass ordering broken chemical property groupings.
  • Rearranged elements based on atomic number and shared chemical properties.
  • Anomalous Mass Pair Example: Tellurium ($\text{Te}$) has a higher atomic mass than Iodine ($\text{I}$). Mendeleev deliberately placed Tellurium to the left of Iodine so Iodine aligned in the same group as Fluorine, Chlorine, and Bromine based on halogen reactivity.
  • Predictive Power (Eka-aluminum): Left deliberate gaps in the table for undiscovered elements.
  • In 1871, he predicted the existence of "Eka-aluminum" (Sanskrit "eka" meaning one/first below aluminum), predicting its density ($6\,\text{g/cm}^3$), low melting point, and atomic weight.
  • Gallium ($\text{Ga}$) was discovered years later with physical properties matching Mendeleev's exact predictions, validating his periodic structure.