2.1 Evolution of Atomic Theory, Subatomic Particles & Mass Spectrometry

2.1 Evolution of Atomic Theory, Subatomic Particles & Mass Spectrometry

Modern atomic theory evolved through experiments that dismantled the concept of indivisible atoms, establishing subatomic structure, quantized charge, and isotopic variations.

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Historical Progression of Atomic Models

Dalton's Model and Limitations

In 1808, John Dalton formulated the first modern atomic theory:

1. Matter consists of indivisible atoms.
2. All atoms of a given element share identical mass and properties.
3. Compounds form when atoms combine in fixed whole-number ratios.
4. Chemical reactions rearrange atoms without creating or destroying them.

Subsequent discoveries modified Dalton's postulates: subatomic particles proved atoms are divisible; isotopes demonstrated that atoms of the same element differ in mass; and nuclear reactions can transmute elements.

Cathode Rays and the Electron

In 1897, J.J. Thomson investigated electrical discharges in evacuated cathode ray tubes. High voltage generated a ray traveling from the negative cathode to the positive anode. The ray was deflected toward positive electric plates and deflected by magnetic fields, confirming it consisted of negatively charged particles—electrons. Thomson measured their charge-to-mass ratio:

e/m_e = -1.759 × 10¹¹ C/kg

Because this ratio far exceeded that of hydrogen ions, Thomson concluded electrons are universal subatomic constituents, proposing the plum pudding model of electrons embedded in a positive sphere.

Millikan's Oil Drop Experiment

In 1909, Robert Millikan determined the electron's charge by suspending X-ray ionized oil droplets between charged plates. Balancing electrostatic force with gravity (qE = mg) showed each droplet's charge was an integer multiple of a fundamental unit:

e = -1.602 × 10⁻¹⁹ C

Combining e with Thomson's ratio yielded the electron's rest mass:

m_e = (-1.602 × 10⁻¹⁹ C) / (-1.759 × 10¹¹ C/kg) = 9.109 × 10⁻³¹ kg (5.486 × 10⁻⁴ amu)

Rutherford's Nuclear Atom

In 1911, Ernest Rutherford bombarded ~400 nm gold foil with alpha particles (⁴₂He²⁺). While >99.9% passed straight through, ~1 in 8,000 scattered at angles >90°, some bouncing backward. Rutherford concluded the atom is mostly empty space with all positive charge and nearly all mass concentrated in a tiny, dense central nucleus (~10⁻¹⁵ m vs. ~10⁻¹⁰ m for the atom).

Discovery of the Neutron

Because nuclear charge accounted for only half of atomic mass, James Chadwick in 1932 bombarded beryllium-9 with alpha particles:

⁹₄Be + ⁴₂He --> ¹²₆C + ¹₀n

The resulting neutral radiation ejected protons from paraffin wax, confirming the neutron (mass 1.00866 amu).

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Subatomic Particles and Nuclide Notation

• Atomic Number (Z): Number of protons; defines the element.
• Mass Number (A): Total nucleons (protons + neutrons): A = Z + N.
• Isotopes: Atoms of the same element (identical Z) with different neutron numbers (different A). They have essentially identical chemical reactivity but differ in mass and nuclear stability.
• Nuclide Symbol: ᴬ_Z X^(±q), where X is the elemental symbol and q is net charge.

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Quantitative Isotopic Abundances & Average Atomic Mass

Standard atomic weight is the abundance-weighted average of all natural stable isotopes:

A_avg = Σ (f_i × m_i) = (f₁ × m₁) + (f₂ × m₂) + ...

Worked Example 1: Chlorine

Chlorine consists of ³⁵Cl (34.969 amu, 75.78%) and ³⁷Cl (36.966 amu, 24.22%):

A_avg = (0.7578 × 34.969) + (0.2422 × 36.966) = 26.499 + 8.953 = 35.45 amu

Worked Example 2: Copper Abundances

Copper (63.546 amu) contains ⁶³Cu (62.930 amu) and ⁶⁵Cu (64.928 amu). Letting x equal the fraction of ⁶³Cu:

63.546 = 62.930x + 64.928(1 - x) = 64.928 - 1.998x 1.998x = 1.382 ==> x = 0.6917 (69.17% ⁶³Cu, 30.83% ⁶⁵Cu)

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Determining Atomic Masses: Chemical and Physical Means

The CLEP outline asks how atomic masses were determined "by chemical and physical means." The two routes answer different questions.

Chemical means (nineteenth-century methods)

• Combining masses (equivalent mass): Weigh how much of an element combines with a fixed mass of a reference element. The equivalent mass is the mass of an element that combines with $8.00\text{ g}$ of oxygen. Atomic mass = equivalent mass × valence, so the valence (combining capacity) must be known or deduced.
• Dulong–Petit rule: For many solid metallic elements, the molar heat capacity is roughly $25\text{ J/(mol}\cdot\text{K)}$. Dividing $25$ by the measured specific heat gives an approximate atomic mass, which fixes the valence needed to turn an exact equivalent mass into an exact atomic mass.
• Gas densities and Avogadro's hypothesis (Cannizzaro's method): Equal volumes of gases contain equal numbers of molecules, so gas densities give molar masses of volatile compounds. The smallest mass of an element found in one mole of any of its compounds approximates that element's atomic mass.

Worked Example: Combining Masses + Dulong–Petit

A metal oxide is $79.89\%$ metal by mass, and the metal's specific heat is $0.39\text{ J/(g}\cdot^\circ\text{C)}$.

1. Approximate atomic mass (Dulong–Petit): $25 / 0.39 \approx 64\text{ g/mol}$.
2. Equivalent mass: $(79.89 / 20.11) \times 8.00 = 31.78\text{ g}$ of metal per $8.00\text{ g}$ of O.
3. Valence: $64 / 31.78 \approx 2$, so atomic mass $= 2 \times 31.78 = 63.56\text{ g/mol}$ (copper, in CuO).

Physical means (modern method)

Mass spectrometry (below) measures the mass of each isotope and its relative abundance directly; the weighted average of those isotope masses is the standard atomic weight printed on the periodic table.

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Mass Spectrometry

Mass spectrometry (MS) measures isotopic masses and abundances through five stages:

1. Vaporization: Sample is converted into low-pressure gas.
2. Ionization: Electron bombardment knocks out electrons, forming cations: M(g) + e⁻ --> M⁺(g) + 2e⁻.
3. Acceleration: Electric potential V accelerates ions to uniform kinetic energy: KE = qV = (1/2)mv².
4. Deflection: Magnetic field B exerts Lorentz force (qvB = mv²/r), yielding radius r = (1/B)√(2Vm/q). Lighter ions deflect more (smaller r).
5. Detection: Ion currents generate peak intensities proportional to relative abundances.

Halogen Mass Spectra Patterns

• Chlorine (Cl₂): Monatomic peaks appear at m/z 35 and 37 (3:1 ratio). Diatomic Cl₂⁺ ions yield three peaks from binomial expansion (3/4 + 1/4)²: m/z 70 (³⁵Cl₂⁺), 72 (³⁵Cl³⁷Cl⁺), and 74 (³⁷Cl₂⁺) in a 9 : 6 : 1 ratio.
• Bromine (Br₂): Monatomic ⁷⁹Br and ⁸¹Br appear in a 1:1 ratio. Diatomic Br₂⁺ ions yield peaks at m/z 158, 160, and 162 in a 1 : 2 : 1 ratio ((1/2 + 1/2)²).