Option B matches the standard form for the quadrupole moment derived for an ellipsoidal charge distribution with the given symbols.

Using λ = h/(mv) with m = 5.0 mg = 5.0×10^-6 kg and v = 8 m/s gives λ ≈ 6.63×10^-34/(4×10^-5) ≈ 1.65×10^-29 m.

Due to binding energy (mass defect), the nucleus mass is less than the sum of its separate nucleons' masses.

The Brackett series corresponds to transitions terminating at n=4, so setting n=4 in the general formula yields the Brackett series; the OCR shows option D marked.

The well-known Pauli-matrix identity states (σ·A)(σ·B) = (A·B) + i σ·(A×B), which is the correct identity used in spin-orbit/Darwin term derivations.

Canal rays (positive rays) are streams of positive ions; thus they are positively charged particles.

α-particles are massive and leave thick short tracks, β-particles are lighter leaving thin long tracks, and γ-rays produce fuzzy or no definite tracks, so B matches.

de Broglie λ = h/(mv) ≈ 6.626×10^-34 / (9.11×10^-31 × 10^6) ≈ 7.3×10^-10 m, closest to 7.0×10^-10 m.

Carbon (mass 12) has 6 neutrons and silicon (mass 28) has 14 neutrons, giving a neutron ratio of 6:14 which reduces to 3:7, so option A is correct.

The OCR answer key indicates option C as the selected answer in the source text.