Atomic Structure A-Z

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1. Fundamental Particles Proton ($p^+$): Charge: $+1.602 \times 10^{-19}$ C (or $+1$ e) Mass: $1.672 \times 10^{-27}$ kg (or $1.007$ amu) Location: Nucleus Neutron ($n^0$): Charge: $0$ Mass: $1.674 \times 10^{-27}$ kg (or $1.008$ amu) Location: Nucleus Electron ($e^-$): Charge: $-1.602 \times 10^{-19}$ C (or $-1$ e) Mass: $9.109 \times 10^{-31}$ kg (or $0.0005$ amu) Location: Orbitals/Electron Cloud 2. Atomic Number & Mass Number Atomic Number ($Z$): Number of protons in the nucleus. Defines the element. For a neutral atom, $Z = \text{number of electrons}$. Mass Number ($A$): Total number of protons and neutrons in the nucleus. $A = Z + \text{number of neutrons}$. Notation: $^A_Z X$ or $^A X$ (where $X$ is element symbol) 3. Isotopes, Isobars, Isotones Isotopes: Atoms of the same element ($Z$ is same) but with different numbers of neutrons ($A$ is different). Example: $_6^{12}C$, $_6^{13}C$, $_6^{14}C$ Isobars: Atoms of different elements ($Z$ is different) but with the same mass number ($A$ is same). Example: $_{18}^{40}Ar$, $_{19}^{40}K$, $_{20}^{40}Ca$ Isotones: Atoms of different elements with the same number of neutrons ($A-Z$ is same). Example: $_{11}^{23}Na$ ($12n$), $_{12}^{24}Mg$ ($12n$) 4. Atomic Models Dalton's Atomic Theory (1803): Atoms are indivisible, indestructible. All atoms of an element are identical. Atoms combine in whole number ratios. Thomson's Plum Pudding Model (1904): Atom is a sphere of positive charge with electrons embedded. Rutherford's Nuclear Model (1911): Gold foil experiment. Dense, positively charged nucleus at the center. Electrons orbit the nucleus. Most of the atom is empty space. Bohr's Model (1913): Electrons orbit in specific, quantized energy levels (shells). Electrons do not radiate energy in these stable orbits. Energy is absorbed/emitted when electrons move between levels ($E=h\nu$). $E_n = -13.6 \frac{Z^2}{n^2}$ eV (for H-like atoms) Quantum Mechanical Model (Schrödinger, 1926): Electrons exist in orbitals, not fixed orbits. Orbitals are regions of probability for finding an electron. Based on wave-particle duality. 5. Quantum Numbers Principal Quantum Number ($n$): Defines main energy level/shell. $n = 1, 2, 3, ...$ Higher $n$ means higher energy and larger orbital. Azimuthal/Angular Momentum Quantum Number ($l$): Defines shape of orbital (subshell). $l = 0, 1, ..., n-1$ $l=0 \rightarrow s$ (spherical), $l=1 \rightarrow p$ (dumbbell), $l=2 \rightarrow d$ (complex), $l=3 \rightarrow f$ (more complex) Magnetic Quantum Number ($m_l$): Defines orientation of orbital in space. $m_l = -l, ..., 0, ..., +l$ Number of orbitals in a subshell is $2l+1$. Spin Quantum Number ($m_s$): Defines intrinsic angular momentum (spin) of electron. $m_s = +\frac{1}{2}$ or $-\frac{1}{2}$ 6. Electronic Configuration Principles Aufbau Principle: Electrons fill orbitals of lowest energy first. Pauli Exclusion Principle: No two electrons in an atom can have the same set of four quantum numbers ($n, l, m_l, m_s$). Max 2 electrons per orbital, with opposite spins. Hund's Rule of Maximum Multiplicity: When filling degenerate orbitals, electrons fill each orbital singly with parallel spins before pairing up. Stability of Half-filled/Fully-filled Orbitals: Extra stability due to symmetry and exchange energy. Example: $Cr$ is $[Ar]3d^5 4s^1$ (not $3d^4 4s^2$) Example: $Cu$ is $[Ar]3d^{10} 4s^1$ (not $3d^9 4s^2$) 7. Rules for Filling Orbitals (n+l rule) Orbitals are filled in increasing order of $(n+l)$ value. If two orbitals have the same $(n+l)$ value, the one with lower $n$ is filled first. $1s \quad (1+0=1)$ $2s \quad (2+0=2)$ $2p \quad (2+1=3)$ $3s \quad (3+0=3)$ $3p \quad (3+1=4)$ $4s \quad (4+0=4)$ $3d \quad (3+2=5)$ $4p \quad (4+1=5)$ $5s \quad (5+0=5)$ $4d \quad (4+2=6)$ $5p \quad (5+1=6)$ $6s \quad (6+0=6)$ $4f \quad (4+3=7)$ $5d \quad (5+2=7)$ 8. Atomic Spectra Emission Spectrum: Light emitted when electrons fall from higher to lower energy levels. Discrete lines. Absorption Spectrum: Light absorbed when electrons jump from lower to higher energy levels. Dark lines on a continuous spectrum. Rydberg Formula for Hydrogen: $$ \frac{1}{\lambda} = R_H \left( \frac{1}{n_1^2} - \frac{1}{n_2^2} \right) $$ where $R_H = 1.097 \times 10^7 \text{ m}^{-1}$ (Rydberg constant), $n_1 Series: Lyman ($n_1=1$, UV) Balmer ($n_1=2$, Visible) Paschen ($n_1=3$, IR) Brackett ($n_1=4$, IR) Pfund ($n_1=5$, IR) 9. Dual Nature of Matter (De Broglie) All matter exhibits wave-like properties. De Broglie Wavelength: $\lambda = \frac{h}{p} = \frac{h}{mv}$ $h$: Planck's constant ($6.626 \times 10^{-34}$ J s) 10. Heisenberg's Uncertainty Principle It is impossible to precisely determine simultaneously both the position and momentum of a particle. $\Delta x \cdot \Delta p \ge \frac{h}{4\pi}$ $\Delta x$: uncertainty in position $\Delta p$: uncertainty in momentum 11. Ionization Energy (IE) Minimum energy required to remove the most loosely bound electron from a gaseous atom in its ground state. $X(g) \rightarrow X^+(g) + e^-$ Factors: Atomic size (inverse), Nuclear charge (direct), Shielding effect (inverse), Penetration effect, Half/fully-filled orbitals. Successive IEs increase ($IE_1 12. Electron Affinity (EA) Energy released when an electron is added to a neutral gaseous atom to form a negative ion. $X(g) + e^- \rightarrow X^-(g)$ Generally increases across a period and decreases down a group. Halogens have high EA. Noble gases and alkaline earth metals have very low/positive EA. 13. Electronegativity (EN) Tendency of an atom in a molecule to attract shared electron pairs towards itself. No units. Relative scale (Pauling scale). Increases across a period, decreases down a group. Fluorine (4.0) is the most electronegative element. 14. Atomic Radius Distance from the center of the nucleus to the outermost electron shell. Decreases across a period (increasing $Z_{eff}$), increases down a group (increasing $n$). Covalent Radius: Half the distance between nuclei of two identical atoms bonded covalently. Metallic Radius: Half the internuclear distance between two adjacent metal atoms in a metallic lattice. Van der Waals Radius: Half the internuclear distance between two non-bonded atoms in separate molecules. 15. Ionic Radius Radius of an ion. Cations: Smaller than parent atom (loss of electron, increased $Z_{eff}$). Anions: Larger than parent atom (gain of electron, decreased $Z_{eff}$, increased electron-electron repulsion). Isotronic series: Ions with the same number of electrons. Size decreases with increasing nuclear charge (e.g., $N^{3-} > O^{2-} > F^- > Na^+ > Mg^{2+} > Al^{3+}$).