(a) Ethanolic solution of compound I on irradiation leads to the formation of compounds II, III and IV [structures in the paper…

(a) I is verbenone (4,6,6-trimethylbicyclo[3.1.1]hept-3-en-2-one). Irradiation in ethanol first causes a photochemical [1,3]-shift: the excited enone breaks the allylic cyclobutane C–C bond to the CMe₂ bridge, giving a tertiary radical and an allyl radical delocalised onto the carbon α to C=O; recombination at that terminus moves the CMe₂ bridge and gives chrysanthenone II, in which the carbonyl sits in a four-membered ring and the C=C is no longer conjugated with it. II absorbs further: α-cleavage of the cyclobutanone followed by β-scission opens the skeleton to a dienyl ketene, which ethanol traps (EtOH adds across C=C=O) to give ethyl 3,7-dimethylocta-3,6-dienoate IV (β,γ-unsaturated) and its conjugated isomer, ethyl 3,7-dimethylocta-2,6-dienoate III. The irradiated mixture therefore contains residual I plus II, III and IV, each giving one C=O band.

Reference values: saturated open-chain or six-ring ketone ≈ 1715 cm⁻¹; saturated ester ≈ 1735–1750 cm⁻¹; conjugation lowers ν by ≈ 20–35 cm⁻¹; a four-membered ring raises a ketone by ≈ 65–70 cm⁻¹.

• 1787 cm⁻¹ → II (chrysanthenone). A cyclobutanone C=O (cyclobutanone itself ≈ 1780–1785). The small internal C–C(O)–C angle puts more p-character into the ring bonds and more s-character into the C=O σ bond, stiffening it; the C=C is β,γ, so there is no conjugative lowering.
• 1740 cm⁻¹ → IV. An ester whose C=C is β,γ (a CH₂ separates it from C=O), so it behaves as an ordinary saturated ester: the −I effect of the alkoxy oxygen outweighs its +M donation and raises ν above that of a ketone.
• 1715 cm⁻¹ → III. The same ester group, now conjugated with the α,β-C=C; delocalisation (C=C–C=O ↔ ⁺C–C=C–O⁻) gives the C=O more single-bond character and lowers ν by ≈ 25 cm⁻¹ (α,β-unsaturated esters absorb at 1715–1730 cm⁻¹).
• 1685 cm⁻¹ → I (unreacted verbenone). A conjugated cyclohexenone (≈ 1675–1690 cm⁻¹); conjugation lowers ν from the 1715 cm⁻¹ of a saturated six-ring ketone.

Order of frequency: II (strained, unconjugated ketone) > IV (unconjugated ester) > III (conjugated ester) > I (conjugated ketone).

(b)(i) Methoxide attacks the very electrophilic carbonyl of 2,2-dimethylcyclopropanone (an sp² carbon forced into a 60° ring) to give a tetrahedral hemiketal alkoxide. The alkoxide re-forms C=O and expels one ring carbon as a carbanion, relieving the ring strain (Favorskii-type ring opening). Two bonds can break:

• Path a (C1–C3): the leaving carbon is the unsubstituted CH₂, a primary (more stable) carbanion; protonation by methanol gives methyl 2,2-dimethylpropanoate (methyl pivalate), (CH₃)₃C–COOCH₃.
• Path b (C1–C2): the leaving carbon is the CMe₂, a less stable tertiary carbanion; this would give methyl 3-methylbutanoate, (CH₃)₂CH–CH₂–COOCH₃, the other possible product.

The data fit methyl pivalate (C₆H₁₂O₂, M = 116):

• IR: 1740 cm⁻¹ is a saturated ester C=O; 1160 cm⁻¹ is the C–O–C stretch.
• ¹H NMR: δ 3.6 (3H, s) is the ester OCH₃; δ 1.2 (9H, s) is a tert-butyl group, nine equivalent protons with no neighbouring H. There is no CH₂ or CH signal, which rules out methyl 3-methylbutanoate (that would show δ ≈ 2.2, d, 2H; ≈ 2.1, m, 1H; ≈ 0.95, d, 6H).
• MS: m/z 116 is M⁺•; 85 = M − •OCH₃ (31), the acylium ion (CH₃)₃C–C≡O⁺; 59 = M − •C(CH₃)₃ (57), ⁺CO₂CH₃; 31 = CH₃O⁺. (m/z 57, (CH₃)₃C⁺, is also strong.)

(b)(ii) I is (E)-methyl crotonate (Ha and Hb on adjacent alkene carbons, trans); II is methyl methacrylate (Ha and Hb on the same =CH₂ carbon, geminal); III is (Z)-methyl crotonate (Ha and Hb on adjacent carbons, cis).

• Geminal =CH₂ coupling (²J) is small, ≈ 0–3 Hz (≈ 1–2 Hz in methyl methacrylate).
• Vicinal ³J depends on the H–C=C–H dihedral angle (Karplus relation): 0° (cis) gives ≈ 6–12 Hz (≈ 11–12 Hz in the Z-ester); 180° (trans) gives the best orbital overlap and the largest value, ≈ 12–18 Hz (≈ 15–16 Hz in the E-ester).

Increasing J(Ha–Hb): II < III < I.

(c)(i) Loss of HCl from (CH₃)₂CCl–CH(CH₃)₂ can remove a β-H from the CH (Zaitsev) or from a CH₃ (Hofmann):

• 2,3-Dimethylbut-2-ene, (CH₃)₂C=C(CH₃)₂: tetrasubstituted, the major product with a small base such as EtO⁻.
• 2,3-Dimethylbut-1-ene, CH₂=C(CH₃)–CH(CH₃)₂: terminal, favoured with a bulky base such as t-BuO⁻.

¹H NMR: the but-2-ene has four equivalent methyls and no vinylic H, so it shows one singlet at δ ≈ 1.65 (12H). The but-1-ene shows two vinylic =CH₂ signals at δ ≈ 4.65 and 4.70 (1H each), an allylic CH septet at δ ≈ 2.25 (1H), a vinylic CH₃ singlet at δ ≈ 1.72 (3H) and an isopropyl doublet at δ ≈ 1.03 (6H).

IR: the but-1-ene shows =C–H stretch at ≈ 3080 cm⁻¹, a medium C=C stretch at ≈ 1645 cm⁻¹ and the strong =CH₂ out-of-plane wag at ≈ 890 cm⁻¹. The but-2-ene has no =C–H band above 3000 cm⁻¹; because it is symmetrical, its C=C stretch (≈ 1670 cm⁻¹) causes almost no dipole change and is very weak or absent.

(c)(ii) Diethyl ether, CH₃CH₂–O–CH₂CH₃, M = 74:

• m/z 74: molecular ion M⁺•, formed by removing a non-bonding electron from oxygen.
• m/z 59: α-cleavage (of the C–C bond next to O⁺•) expels CH₃•, giving the resonance-stabilised oxonium ion CH₃CH₂–O⁺=CH₂.
• m/z 45: cleavage of a C–O bond with loss of C₂H₅• gives C₂H₅O⁺, which rearranges to the stable CH₃CH=OH⁺.
• m/z 31: the m/z 59 ion transfers an H from its ethyl group to O and loses ethene (C₂H₄, 28) to give CH₂=OH⁺, the base peak.
• m/z 29: inductive (heterolytic) C–O cleavage with the charge on carbon gives the ethyl cation C₂H₅⁺.

(c)(iii) For H³⁵Cl, the reduced mass μ = m_H·m_Cl/(m_H + m_Cl) = (1.008 × 34.97)/(35.98) amu = 0.980 amu = 0.980 × 1.661 × 10⁻²⁷ kg = 1.627 × 10⁻²⁷ kg.

Since I = μr², r = √(I/μ) = √(2.70 × 10⁻⁴⁷ / 1.627 × 10⁻²⁷) m = √(1.660 × 10⁻²⁰) m = 1.29 × 10⁻¹⁰ m.

Bond length r(H–Cl) ≈ 1.29 Å (129 pm). Using m_H = 1 and m_Cl = 35.5 amu gives μ = 1.616 × 10⁻²⁷ kg and the same 1.29 Å; the accepted value is 1.275 Å.