4. (1) (a) I = 1/2 (I = 1/2) I 0 p ( ), n () I = 0 (p + n) I = (1/2, 3/2, 5/2 ) p ( ), n () I = (1, 2, 3 ) (b) (m) (I = 1/2) m = +1/2, 1/2 (I = 1/2) m = +1/2, 1/2 I m = +I, +(I 1), +(I 2) (I 1), I ( ) m m (2) (a) 1/2 ( 1 H, 13 C, 19 F, 31 P, etc.) B 0 (m = +1/2) (m = 1/2) B 0 ΔE ΔE = µ B B 0 = γ (h/2π) B 0 µ B : γ: () h: ν hν m = +1/2 1 H ν = ΔE/h m = 1/2 m = +1/2 1/2 1 H N (m = +1/2) /N (m = 1/2) = exp(δe/kt) k: T: 2.35 T, 17 C (290 K) N (m = +1/2) /N (m = 1/2) 2.35 T 1 H 100MHz ΔE = (6.6 10 34 ) (100 10 6 ) = 6.6 10 26 (J) ΔE/kT = (6.6 10 26 ) (1.38 10 23 290) = 0.000017 ΔE/kT exp(x) 1 + x N (m = +1/2) /N (m = 1/2) = 1 + 0.000017 = 1.000017 (= 1,000,017/1,000,000) 2,000,017 1 H 17 m = +1/2 1
(b) 1 I = 1 D, etc. 3 I = 3/2 7 Li, 11 B, etc. 4 I = n/2 n+1 (3) (NMR) (a) (i) (a) (ii) (b)!"#$%&'()*+,-."#$*+/01234 (i) B 0 (a) m = 1/2, +1/2 2 (ii) (ν = ΔE/h) () (iiʼ) (b) m = 1/2, +1/2 NMR (ii ) (a) (b) 2 (4) (a) B eff B eff = B 0 σb 0 B 0 : σ: νʼ ΔE = hνʼ = γ (h/2π) B eff νʼ = γ/2π (1 σ) B 0 B 0 B 0 σ 0 ν 0 ν 0 = γ/2π (1 σ 0 ) B 0 Δν Δν = νʼ ν 0 = γ/2π (σ 0 σ) B 0 (b) δ δ = 10 6 (Δν/ν) = 10 6 (σ 0 σ) ( : ppm) ν: (= γ/2π B 0 ). 1 H 100 MHz (TMS) 120 Hz δ δ = 10 6 [120/(100 10 6 )] = 1.2 (ppm)
(5) (a) (i) 2 A X (a) (b) ## E #" 1 "# "" 2 4 3 1 2 4 3 B 0 (b) (i) NC C CN H 1 H 2 H 1 H 2 H 1 H 2 (ii) O NC CH 2 CH 2 C OCH 3 H H!A!X!A!X 1, 2 A 3, 4 X (a) A X 1 2 3 4 A, X 1 1 (b) A X A X ΔE ΔE 1 2, 3 4 A, X 2 1 2 3 4 4ΔE (b) A X (J) 1 H NMR J (Hz) J = Δν = 4ΔE/h H H (iii) A m X (m 2I X + 1) (I X : X ) CH 3 CH 2 Br CH 3 H CH 3 2 2 (1/2)+1 = 3 CH 2 H 3 2 (1/2)+1 = 4 n A m X A (m 2I X + 1) X (n 2I A + 1) A n X m (or A n B m, A n M m ) (X: ν A ν X B: ν A ν B M: ν A ν M ) 3
A n X 2 (A, X I = 1/2 n ) A (a) E 2 4 3!A!X!A!X A X (b) (a) A E A 1 4 E 1 E 4 2 & 3 1 E 1 = E + 2ΔE 2 & 3 E 2 or E 3 = E 4 E 4 = E 2ΔE 1 4 A NMR 1 : 2 : 1 p. 74 3.2 I = 1/2 n n + 1 (b) 1 2 (iv) A m X l M J A X J A M (m 2I X + 1) (l 2I M + 1) O C C 6 H 5 H CH 1 2H3 H 2 H 1, H 3 H 2 (1+1) (1+1) = 4 A J A X = 8 Hz, J A M = 6 Hz J A M J A X J A M./0123456789 ::::::::+,-;<!X"#$%&!M"#$%& '()*$+,- (6) NMR CH 3 CH 2 Br CH 3 CH 2 3 : 2 4
5. 1 H NMR (1) 1 H NMR (b) 1 H NMR (2) 1 H NMR (a) NMR ( 5 mm ) 1 10 mg 1 cm 3 4 0.6 ml NMR CDCl 3 ( -d) TMS (SiMe 4, 0.01% ) D 2 O C 6 D 6 CD 3 OD, -d 6 THF-d 8, CD 2 Cl 2, etc. ( 10,000/ ) CCl 4, CS 2 (NOE ) TMS 0 ppm TMS TMS J (Hz) = (ppm) (MHz) ( )H 1 H NMR 5
(c) (i) 1 H NMR (ii) 1 H NMR! : CH > CH 2 > CH 3 ( )! : F CH > O CH > N CH 0.5 1.6 ppm 1.6 3.0 ppm C=C, C=O, 3.0 5.0 ppm 5.0 6.0 ppm 6.0 8.5 ppm 9.0 11.0 ppm OH, NH, COOH π- π- π + (iii) p 116 118 6
(d) (J) (i) H J m H m+1 p 74 1-propanol (iii) ( 2 J H H ) H ( 3 J H H ) H (e) H J m H n H (m+1) (n+1) p 74 H J J H (ii) Karplus p 103, 3.34 3 J φ 3 J = 8.5 cos 2 φ 0.28 (0 φ 90 ) CO 2 H H H CO 2 H H H H CO H H 2 H HO 2 C H 3-phenylpropionic acid A B C CO 2 H H 2 N H L-phenylalanine CO 2 H H NH 2 H H 2 N CO 2 H NH 2 HO 2 C H X Y Z H a H b (A) or (B, C) H a, H b H a H b (X, Y, Z) H a, H b = 9.5 cos 2 φ 0.28 (90 φ 180 ) 7
(f) 1 H NMR ( p 74, 3.2 ) d doublet, t triplet, q quartet, dd double doublet, dt double triplet ddd, ddt td 8