Atomic Structure

Ancient Concept: Democritus suggested matter is made of indivisible particles called atoms.

Dalton's Atomic Theory (1808): John Dalton proposed that atoms are indivisible hard spheres. Elements are composed of atoms.

Modern View: Atom is divisible into subatomic particles: Electrons, Protons, Neutrons.

Experiment (1879): Sir William Crookes performed experiments in a discharge tube at very low pressure. When high voltage was applied, rays were emitted from the cathode.

Properties of Cathode Rays:

• Travel in straight lines perpendicular to cathode surface.
• Cast a sharp shadow of an opaque object (proven they are material particles).
• Deflected towards positive plate in electric field (proven they are negatively charged).
• Raise temperature of body they fall on.
• J.J. Thomson (1897) discovered their charge-to-mass (e/m) ratio.
• Conclusion: These rays are electrons. Electrons are fundamental particles of all atoms.

Experiment (1886): Goldstein observed positive rays in a discharge tube with a perforated cathode. These rays passed through the holes (canals) of the cathode.

Origin: Produced when cathode rays collide with residual gas molecules, ionizing them ($M + e^- \to M^+ + 2e^-$).

Properties:

• Travel in straight lines opposite to cathode rays.
• Deflected towards negative plate in electric field (positively charged).
• Mass varies with the nature of gas in the tube.
• Hydrogen gas produces the lightest positive particles, called Protons (mass = 1836 times electron).

Discovery (1932): Sir James Chadwick discovered neutrons by bombarding Beryllium with Alpha particles ($\alpha$).

Reaction: $^9_4Be + ^4_2He \to ^{12}_6C + ^1_0n$

Properties:

• Neutral particles (no charge).
• High penetrating power.
• Mass is nearly equal to that of a proton.

Experiment (1911): Rutherford bombarded a very thin Gold Foil ($0.00004$ cm) with Alpha particles produced from Polonium.

Observations:

• Most particles passed through undeflected (Atom is mostly empty space).
• Few were deflected at large angles or bounced back (Presence of massive, positive central body).

Conclusions:

• Nucleus: Small, dense, positively charged center containing almost all atomic mass (Protons+Neutrons).
• Electrons: Revolve around the nucleus.
• Defects: According to classical theory, revolving electrons should emit energy continuously and eventually fall into the nucleus (atom collapse), but atoms are stable. It also couldn't explain line spectrum.

Concept: Based on Max Planck's Quantum Theory. Electrons revolve in fixed circular orbits (shells) with fixed energy (quantized).

Postulates:

• Electrons do not radiate energy while in a stable orbit.
• Energy is absorbed when electron jumps from lower to higher orbit, and emitted when it falls back (${\Delta}E = E_2 - E_1 = h{\nu}$).
• Electrons can only revolve in orbits where angular momentum is integral multiple of $h/2\pi$ ($mvr = nh/2\pi$).

Shells (n): Main energy levels. K (n=1, max 2e), L (n=2, max 8e), M (n=3, max 18e), N (n=4, max 32e). Max electrons = $2n^2$.

Subshells: Sub-division of shells. s (max 2e), p (max 6e), d (max 10e), f (max 14e).

Aufbau Principle/Rule: Electrons fill lowest energy subshells first.

Order: 1s < 2s < 2p < 3s < 3p...

Examples:

• Carbon ($^{12}_6C$): $1s^2, 2s^2, 2p^2$ (K=2, L=4)
• Sodium ($^{23}_{11}Na$): $1s^2, 2s^2, 2p^6, 3s^1$ (K=2, L=8, M=1)
• Chlorine ($^{35}_{17}Cl$): $1s^2, 2s^2, 2p^6, 3s^2, 3p^5$ (K=2, L=8, M=7)

Definition: Atoms of the same element having same atomic number (same protons) but different mass number (different neutrons).

Properties: Same chemical properties (depend on electrons) but different physical properties (depend on mass).

Examples:

• Hydrogen: Protium ($^1_1H$, 0n), Deuterium ($^2_1H$, 1n), Tritium ($^3_1H$, 2n, radioactive).
• Carbon: C-12 (98.9%), C-13 (1.1%), C-14 (Radioactive).
• Chlorine: Cl-35 (75%), Cl-37 (25%).
• Uranium: U-234 (rare), U-235 (0.7%, used in power), U-238 (99%).

• Radiotherapy (Cancer Treatment): P-32 (Blood cancer), Sr-90 (Skin cancer using $\beta$ rays), Co-60 (Body cancer using $\gamma$ rays).
• Tracers (Diagnosis): I-131 (Goiter/Thyroid), Tc-99 (Bone/Brain imaging).
• Archaeological Dating: C-14 (Carbon dating) used to find age of fossils/old objects.
• Power Generation: Uranium-235 fission produces energy for electricity.

Definition: Average mass of atoms of an element as compared to 1/12th the mass of one atom of Carbon-12 ($1 amu = 1.66 \times 10^{-24}g$).

Calculation Formula: Relative Atomic Mass = $\frac{(\text{Mass}_1 \times \%\text{Abundance}_1) + (\text{Mass}_2 \times \%\text{Abundance}_2)}{100}$

Example (Chlorine): $\frac{(35 \times 75) + (37 \times 25)}{100} = 35.5$ amu.