21-Mat-A4 Deformation Behaviour and Properties of Materials · May 2016
Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)
Paper format. National Exams, May 2016 — 10-Met-A4, Structure of Materials. Three hours, closed book, one approved calculator (Casio or Sharp). Eight questions of 20 marks each (Roman numerals I–VIII); the rubric asks for any five, with only the first five in the answer book marked. All eight are solved here, because this set is a study resource rather than an exam script. All necessary equations, constants and an error-function table are provided in the exam's own appendix (reproduced where used below).
Note on the exam title. The printed exam header reads 10-Met-A4, Structure of Materials. Only Question VIII (mechanical deformation) is genuinely deformation/mechanical-properties content; the paper as a whole is a broad introductory materials-science survey — bonding, crystal structure, crystallographic directions/planes, imperfections, phase diagrams, XRD and diffusion — and is answered as such below.
Reference texts. The answers below are keyed to the works normally recommended for this syllabus code:
Question text not reproduced: the examination questions are © Engineers and Geoscientists BC. Open the official past paper (linked at the top of this page) to read the question, then follow the worked solution below.
a. Ground state energy. The ground state is the lowest permitted energy level an electron can occupy in an atom. For a one-electron (hydrogen-like) atom the allowed energies are quantised, $E_n = -Z^2R_E/n^2$, with $R_E=13.61$ eV (the appendix's Rydberg-type constant) and $n=1,2,3,\ldots$; the ground state is $n=1$, giving the most negative (most tightly bound) energy $E_1=-Z^2(13.61\ \text{eV})$. For hydrogen ($Z=1$), $E_1=-13.61$ eV. Any electron promoted to $n>1$ (an excited state) will spontaneously fall back toward $n=1$, emitting a photon of energy $\Delta E=E_i-E_f$.
b. Isotope. Isotopes are atoms of the same element (same atomic number $Z$, same number of protons, hence identical chemistry) that differ in neutron number $N$ and therefore in atomic mass $A=Z+N$. Example: carbon has three natural/common isotopes — $^{12}_{6}\text{C}$ (6 protons, 6 neutrons, 98.9% abundance, stable), $^{13}_{6}\text{C}$ (7 neutrons, stable, used in NMR), and $^{14}_{6}\text{C}$ (8 neutrons, radioactive, $t_{1/2}\approx5730$ yr, used in radiocarbon dating).
c. Electronegativity. Electronegativity is a dimensionless number (Pauling scale, 0.7–4.0) describing an atom's relative ability to attract shared bonding electrons toward itself in a compound. It rises left-to-right across a period (increasing effective nuclear charge, e.g. Li 1.0 → F 4.0) and falls top-to-bottom down a group (increasing atomic radius shields the nucleus, e.g. F 4.0 → I 2.5). A large electronegativity difference between two bonded atoms ($\Delta\chi\gtrsim1.7$) produces an ionic bond (e.g. Na, $\chi=0.9$, with Cl, $\chi=3.0$: $\Delta\chi=2.1$); a small or zero difference produces a covalent bond (e.g. C–C, $\Delta\chi=0$).
The Bohr model (1913) treats the electron as a point particle orbiting the nucleus in fixed, quantised circular orbits of discrete energy $E_n=-Z^2R_E/n^2$, with quantised angular momentum $L=n\hbar$; the electron radiates only when jumping between orbits. It correctly predicted the hydrogen line spectrum but fails for multi-electron atoms (no electron–electron repulsion term), violates the Heisenberg uncertainty principle by assigning the electron a definite classical trajectory, and offers no physical reason for the quantisation — it is simply asserted.
The wave-mechanical (Schrödinger) model treats the electron as a three-dimensional standing wave described by a wavefunction $\psi$; $|\psi|^2$ gives a probability density (an electron-cloud orbital, not a fixed orbit), consistent with the uncertainty principle. Solving the wave equation for a given potential yields four quantum numbers ($n,l,m_l,m_s$, per the appendix) instead of Bohr's one, from which orbital shapes, multi-electron structure (via the Pauli exclusion principle) and the periodic table itself emerge naturally rather than being assumed.
The wave-mechanical model is more accurate: it reproduces everything Bohr's model gets right for hydrogen and additionally predicts multi-electron atomic structure, chemical bonding directionality, and fine spectral structure that Bohr's model cannot address even in principle.
| Material | Intramolecular / lattice bond | What holds the bulk solid together | Melting point |
|---|---|---|---|
| (i) NH₃ | Polar covalent (N–H) | Hydrogen bonds between molecules (secondary) | −78°C |
| (ii) Cl₂ | Nonpolar covalent (Cl–Cl) | Weak van der Waals (secondary) | −101°C (lowest) |
| (iii) MgO | Ionic (Mg²⁺–O²⁻) | Coulombic ionic bonding throughout lattice (primary) | 2852°C |
| (iv) Diamond | Covalent (C–C, sp³) | Covalent network bonding throughout lattice (primary) | ≈3550°C (highest) |
Highest melting point: diamond. Every atom is joined to its neighbours by strong, directional covalent bonds extending through the entire crystal (a covalent network solid) — melting requires breaking primary bonds throughout the lattice. Lowest melting point: Cl₂. Within each Cl₂ molecule the bond is a strong covalent bond, but the molecules themselves are held to one another only by weak secondary (van der Waals/London dispersion) forces, which is what actually breaks on melting. NH₃ also melts at a low (sub-zero) temperature for the same reason, but its intermolecular hydrogen bonding (stronger than pure van der Waals) raises its melting point above Cl₂'s. MgO, an ionic solid with strong non-directional Coulombic bonding through the whole lattice, sits far above both molecular solids but below the covalent network of diamond.
