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# problemset1finalanswers - Problem Set#1 CHEM/BCMB...

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Unformatted text preview: Problem Set #1, CHEM/BCMB 4190/6190/8189 1 Problem Set #1, CHEM/BCMB 4190/6190/8189 1). Which of the following statements are True , False , or Possibly True , for the hypothetical element X? a. The ground state spin is I=0 for 24 52 X . b. The ground state spin is I=0 for 31 70 X . c. The ground state spin is I=1/2 for 21 45 X . d. The ground state spin is I=1 for 22 48 X . e. The ground state spin is I=1/2 for 14 29 X . a. True : both the mass number and the atomic number are even. Therefore, I=0. b. False : the mass number is even and the atomic number is odd. Therefore, I is integral and non-zero. c. Possibly True : the mass number is odd, therefore the spin is half-integral (might be 1/2, might also be 3/2 or 5/2, etc.). d. False : both the mass number and the atomic number are even. Therefore, I=0. e. Possibly True : same rationale as ‘c’. 2). The resonance/precession frequency of a 1 H nucleus ( ¡ 1H ) in a 14.09 T (Tesla) magnet is 600.0 MHz. a. What is the resonance frequency of a 13 C nucleus ( ¡ 13C ) in the same magnet? ( ¢ 1H = 26.7519 x 10 7 rad/Ts, ¢ 13C = 6.7283 x 10 7 rad/Ts). b. What is the resonance frequency of the 1 H nucleus in a 11.74 T magnet? a. ¡ 1H = ¢ 1H 2 £ B and ¡ 13C = ¢ 13C 2 £ B , therefore ¡ 1H ¡ 13C = 600.0 MHz ¡ 13C = ¢ 1H 2 £ ¢ 13C 2 £ B B = ¢ 1H ¢ 13C = 26.7519 ¤ 10 7 6.7283 ¤ 10 7 ¡ 13C = 150.9 MHz b. ¡ 1H, 14.09T ¡ 1H, 11.74 T = 600.0 MHz ¡ 1H, 11.74 T = ¢ 1H 2 £ ¢ 1H 2 £ 14.09 11.74 = 14.09 11.74 ¡ 1H, 11.74 T = 499.9 MHz ¢ 500 MHz Problem Set #1, CHEM/BCMB 4190/6190/8189 2 3). How does the magnitude of the bulk/macroscopic magnetization compare for: a. 1 H and 13 C spins? b. 1 H and 13 C spins at natural abundance (assume the natural abundance of 1 H is 100% and 13 C is 1.11%)? c. 1 H and 17 O spins? ( ¡ 1H = 26.7519 x 10 7 rad/Ts, ¡ 13C = 6.7283 x 10 7 rad/Ts, ¡ 17O = -3.6280 x 10 7 rad/Ts) a. M = N ¡ 2 h 2 B I(I +1) 3k B T (“h” here is “h-bar”, Planck’s constant divided by 2 ¢ ) M 0 1H M 0 13C = N ¡ 1H 2 h 2 B I 1H (I 1H +1) 3k B T N ¡ 13C 2 h 2 B I 13C (I 13C +1) 3k B T = ¡ 1H 2 ¡ 13C 2 = (26.7519 ¢ 10 7 rad/Ts) 2 (6.7283 ¢ 10 7 rad/Ts) 2 = 15.809 So, the bulk magnetization is about 16 times as large for 1 H compared to 13 C, or 13 C magnetization is about 6.3% that of 1 H....
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