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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 nonzero. c. Possibly True : the mass number is odd, therefore the spin is halfintegral (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 hbar, Plancks 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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 Fall '08
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