Atomic Theory and Foundational Experiments – Study Notes

Law of Mass Conservation and Law of Definite Proportions

Early observation: when reacting two substances (e.g., sodium and chlorine to form sodium chloride), the total mass is the same before and after the reaction, regardless of starting amounts or composition changes. This is the law of mass conservation: in any chemical process, mass is conserved.
Example from lecture: starting with 7.7 g Na and 18.9 g Cl yields a total of 19.6 g before reaction, and after the reaction the product mass is still 19.6 g:
- Before: total mass = 7.7 g + 18.9 g = 26.6 g? (note: transcript shows 19.6 g; the key point is that the final mass equals the initial mass of the system being measured). The essential point is: mass at the end equals mass at the start.
Law of mass conservation is a cornerstone for chemical processes and for understanding reactions (mass is neither created nor destroyed).
Law of Definite Proportions (Proust, 1794):
- In a given compound, the elements are always present in a fixed, characteristic proportion by mass, regardless of how the compound was prepared or where it was obtained.
- Example from transcript: sodium chloride (NaCl) analyzed by mass in 100 g samples yields:
- Na: 39.3 g
- Cl: 60.7 g
- Ratio Na:Cl by mass is 39.3:60.7 (for 100 g of NaCl).
- The ratio is constant for that compound; the composition by mass does not depend on the sample’s origin.
Law of Multiple Proportions (Dalton, 1804):
- If two elements A and B form more than one compound, then the masses of B that combine with a fixed mass of A are in simple whole-number ratios.
- Example discussed: carbon monoxide (CO) and carbon dioxide (CO₂) use the same elements (C and O) but in different ratios.
- For CO: mass ratio of O to C ≈
  rac{mO}{mC} ig|_{CO} \,=\, 1.33 \approx \frac{16}{12}
- For CO₂: mass ratio of O to C ≈
  rac{mO}{mC} ig|{CO2} \,=\, 2.67 \approx \frac{32}{12}
- The ratio of these two mass ratios is about 2:
  $\frac{2.67}{1.33} \approx 2$
- This demonstrates that two compounds formed from the same elements have mass ratios that are simple whole numbers, supporting the idea that matter is composed of discrete atoms and combine in fixed whole-number proportions.
Dalton’s Postulates (summary of atomic theory foundations from the lecture):
- Matter is composed of atoms, the smallest unit of matter that retains the properties of an element.
- Elements consist of only one type of atom; different elements have different types of atoms.
- Compounds are formed when atoms of two or more elements combine in simple, whole-number ratios.
- In chemical reactions, atoms are rearranged, not created or destroyed; the number and type of atoms are conserved.
- The mass is conserved in all chemical reactions (connecting to the law of mass conservation).

From Law to Model: Early Atomic Theories

The combination of the laws above provided a framework for atomic theory and the idea that atoms are the building blocks of matter.
The Dalton-based view connected the fixed proportions in compounds to fixed, discrete atoms that participate in reactions, without being destroyed or created in the process.

Key Experiments and the Discovery of Subatomic Structure

Thomson’s Cathode Ray Tube and the Electron (Discovery of the Electron)

Experimental setup: a glass tube with a gas at low pressure, with a cathode (negative plate) and an anode (positive plate).
When a potential difference is applied, a beam travels from the cathode to the anode.
Observations:
- The beam is deflected by magnetic and electric fields, indicating the beam comprises charged particles, not light.
- Deflection shows the particles are negatively charged (attracted to the positive plate).
- The deflection is characteristic of particles with a charge-to-mass ratio e/m that can be measured (the lecture cites approximately $\frac{e}{m_e} = -1.76 \times 10^{11}\ \mathrm{C\;kg^{-1}}$ ).
Conclusions:
- Existence of subatomic particles smaller than atoms: electrons.
- Thomson’s model (the Plum Pudding model): atoms are a positively charged sphere with embedded electrons (the “chips” in a cookie analogy).
- This model explains atom neutrality by balancing positive bulk charge with embedded negative electrons.
Mass and charge implications:
- The electron is far smaller than the hydrogen atom (in terms of the deflected beam, the electron’s size is much smaller than that of a hydrogen atom).
- The experiment established an internal structure of the atom, moving beyond indivisible atoms to subatomic components.

Millikan’s Oil Drop Experiment (Charge of the Electron)

Experimental setup: tiny oil droplets charged by X-ray irradiation pass between two plates (one positive, one negative).
Observations:
- Some droplets could be made to float at a specific plate voltage, balancing gravity with electrostatic force.
- The measured droplets showed charge in discrete multiples of the elementary charge; the pattern of observed charges was quantized.
- The smallest observed charge corresponds to the charge of a single electron, establishing the elementary charge value.
Important outcome:
- Using the charge-to-mass relationship (from Thomson’s ratio), Millikan could deduce the electron mass when combined with charge measurements. This experiment provided a quantitative measure of the electron charge:
- $e = 1.60 \times 10^{-19}\ \mathrm{C}$
- and, together with Thomspon’s ratio, allowed determination of the electron mass (historically, $m_e = 9.11 \times 10^{-31}\ \mathrm{kg}$ , though the transcript focuses on the ratio and charge).
Significance: solidified the reality of discrete electronic charge and provided a fundamental constant used in atomic physics.

Radioactivity and Subatomic Particles: Particles, Antiparticles, and Radiation

Natural radiation types discussed: alpha (α), beta (β), gamma (γ).
- Alpha particles: positively charged, behave like helium-4 nuclei (two protons, two neutrons).
- Beta particles: electrons (β−) or positrons (β+), negative or positive charge, respectively.
- Gamma rays: high-energy photons, no mass or charge.
Rutherford–Gieger (gold foil) experiment context: while revealing the structure of the atom, it also linked to radiation processes used to probe matter.
Important point: gamma rays, while energetic, do not carry charge and interact differently with matter than charged particles.

Rutherford’s Gold Foil Experiment and the Nuclear Model (Discovery of the Nucleus)

Experimental setup: alpha particles directed at a thin foil of gold; observations of how particles passed through or were deflected by the foil.
Observations described in the lecture:
- Approximately 98% of alpha particles passed through with little or no deflection, indicating most of the atom is empty space.
- A small fraction (about 0.5%) were deflected at small angles, indicating the presence of a concentrated positive charge within the atom.
- An extremely small fraction (~0.005%) bounced straight back, implying a very dense, small, positively charged center—the nucleus.
Conclusions:
- The atom has a tiny, dense nucleus containing protons (and, later, neutrons) and is surrounded by mostly empty space where electrons move.
- The nucleus is positively charged (due to protons) and accounts for most of the atom’s mass; electrons contribute negligibly to mass.
- The overall atom is electrically neutral because it contains equal numbers of protons and electrons (in typical neutral atoms).
Analogies used in lecture:
- Football stadium analogy: placing a nucleus at the center of a football field-sized atom illustrates the relative size difference; the nucleus is tiny compared to the atom as a whole (the nucleus is like a marble at the center of a stadium, i.e., the atom’s diameter is ~10^5 times larger than the nucleus).
Be example to illustrate the scale of the nucleus versus the atom:
- If the atom were the size of a stadium, the nucleus would be roughly the size of a marble at the center.
Be-9 nucleus mass discrepancy (nucleon composition):
- Real Be nucleus has Z = 4 protons and A = 9 nucleons in total, implying N = A − Z = 5 neutrons.
- The proton count suggests a theoretical mass of 4 amu from protons, but the observed mass is about 9 amu, indicating neutrons contribute roughly 5 amu of mass without charge.
- This motivated Rutherford’s proposal of a neutral neutron as a second nucleon inside the nucleus (a concept further developed in later work).

Isotopes and Neutron Discovery

Isotopes (Soddy, 1921): atoms of the same element can have different masses but behave chemically the same.
The mass difference in nuclei is explained by the presence of neutrons in the nucleus (neutrons add mass without changing charge).
Neutron discovery and refinement of the atomic model came later with Chadwick (1932), confirming the existence of the neutron and completing the modern view of the nucleus as consisting of protons and neutrons.

Atomic Model and Its Significance

The modern view (as summarized in the lecture):
- Nucleus: dense, positively charged center containing protons (positive charge) and neutrons (neutral mass). Mass of the nucleus is primarily from nucleons; the proton charge determines the positive charge.
- Electron cloud: electrons move around the nucleus in mostly empty space; electron mass is negligible compared to nuclear mass.
- Overall atom: electrically neutral when number of protons equals number of electrons.
The scale relationship:
- Nucleus diameter vs atom diameter is roughly on the order of 1:10^5 to 1:10^6; most of the atom is empty space.
Implications for chemical properties:
- The chemical behavior of an element is governed by electrons and their arrangement around the nucleus.
- Nuclear properties (not typically involved in chemistry) are governed by the numbers of protons and neutrons in the nucleus.

Summary of Key Historical Milestones and Numbers (from the lecture)

Law of Definite Proportions: fixed mass ratios in a given compound; established by Joseph Proust (1794).
Law of Multiple Proportions: mass ratios of two elements forming different compounds are simple whole-number ratios; established by John Dalton (1804).
Dalton’s atomic postulates (summary): matter is made of atoms; atoms of the same element are identical; compounds are formed by whole-number combinations of atoms; atoms rearrange in reactions; mass is conserved.
Thomson’s cathode ray tube: discovered electrons; measured charge-to-mass ratio: $\frac{e}{m_e} = -1.76 \times 10^{11}\ \mathrm{C\,kg^{-1}}).$
Millikan’s oil drop experiment: determined the elementary charge: $e = 1.60 \times 10^{-19}\ \mathrm{C}$ ; electron mass derived in combination with Thomson’s ratio.
Rutherford’s gold foil experiment: discovered the nucleus; evidence for a tiny, dense, positively charged center; most of the atom is empty space; approximate percentages: ~98% pass, ~0.5% deflected, ~0.005% back-scattered.
Nuclear composition and isotopes: Be-9 example illustrating protons vs neutrons; Z = 4, A = 9, N = 5; neutrons explain extra mass without charge.
Isotopes (Soddy, 1921): same element can have different masses but similar chemical behavior; neutrons account for mass differences; Chadwick’s neutron discovery (1932) completed the nuclear model.
Visual analogies used in lectures:
- Plum pudding vs chocolate chip cookie analogy for Thomson’s model: a positively charged matrix with embedded electrons (chips).
- Nucleus-as-marble in a stadium analogy to illustrate the extreme smallness of the nucleus relative to the whole atom.

Connections to Foundations and Real-World Relevance

Foundational principles link macroscopic chemistry (stoichiometry, reactions) with microscopic atomic structure (atoms, electrons, nucleus).
The mass-conservation and fixed-proportion laws underpin stoichiometry calculations used in chemistry labs and industry.
The discovery of subatomic particles (electron, proton, neutron) laid the groundwork for modern physics and nuclear science, with broad practical implications in energy, medicine, imaging, and materials science.

Ethical, Philosophical, and Practical Implications (as discussed in the lecture)

The transcript focuses on historical experiments and scientific concepts; it does not deeply address ethics or philosophy.
Practical implications of atomic theory emerged later (nuclear energy, radiography, medical imaging, radiation safety), but those topics are outside the scope of this lecture excerpt.

Notation and Formulas to Remember (LaTeX)

Law of Mass Conservation: $m{ ext{initial}} = m{ ext{final}}$
Law of Definite Proportions: In a compound AB, the ratio of masses is constant: $\frac{mA}{mB} = \text{constant}$
Law of Multiple Proportions: For compounds formed from elements A and B, the mass ratios are simple integers: if compounds C1 and C2 have masses $\frac{mB}{mA}\bigg|{C1} = r1$ and $\frac{mB}{mA}\bigg|{C2} = r2$ , then $\frac{r2}{r1} \in \mathbb{N}$
Electron charge-to-mass ratio ( Thomson ): $\frac{e}{m_e} = -1.76 \times 10^{11}\ \mathrm{C\,kg^{-1}}$
Elementary charge (Millikan): $e = 1.60 \times 10^{-19}\ \mathrm{C}$
Carbon monoxide and carbon dioxide mass ratios:
- CO: $\frac{mO}{mC} \big|_{CO} = \frac{16}{12} \approx 1.33$
- CO₂: $\frac{mO}{mC} \big|{CO2} = \frac{32}{12} \approx 2.67$
- Ratio of these two: $\frac{2.67}{1.33} \approx 2$
Nuclear composition example (Be-9): Z = 4, A = 9, hence N = A - Z = 5, mass ~ 9 amu (neutrons add mass without charge)
Size scale (nucleus vs atom): rough visual aid: nucleus diameter ≈ 10^{-5} of atom diameter; nucleus is tiny and atom is mostly empty space

Quick Reference Timeline

1794: Law of Definite Proportions (Joseph Proust)
1804: Law of Multiple Proportions (Dalton)
Late 1800s: Thomson discovers electron and proposes Plum Pudding model
1909–1913: Millikan measures elementary charge; refines e/m ratio
1911: Rutherford discovers the nucleus via gold foil experiment
1921: Isotopes concept introduced (Soddy)
1932: Neutron discovered (Chadwick)