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Unformatted text preview: Name _________________________ Exam 1, 2010: CHEM/BCMB 4190/6190/8189 1 Exam 1: CHEM/BCMB 4190/6190/8189 (108 points) Thursday, 9 September, 2010 1 ). The symbol I is used to represent the angular momentum quantum number or spin quantum number (or just “spin”) of a particle. a. Describe in words what is defined by the spin quantum number I . ( 4 points ) The spin quantum number I defines the number of allowed energy levels or spin states that a nucleus can occupy in the presence of a magnetic field (2 I +1). b. What values of m , the magnetic or directional quantum number, are allowed for 133 Cs in a magnetic field? ( 4 points ) Values of m are given by m = (- I , - I +1, …, I-1, I ). For 59 Co, I = 7/2, so the possible values for m are -7/2, -5/2, -3/2, -1/2, 1/2, 3/2, 5/2, and 7/2. c. In a magnetic field where the resonance frequency of 133 Cs is 52.468 MHz, calculate the energy difference between the highest and lowest energy levels of 133 Cs. ( 6 points ) For a nucleus with I > 0, in a magnetic field the energy difference between any two adjacent energy levels, ΔΕ , is given by . For 133 Cs, with spin=7/2, there are 8 energy levels, so the energy difference between the lowest and highest is equal to 7 times the difference between any two adjacent levels ( ). The value of γ for 133 Cs is 3.5339 × 10 7 rad/T/s. The resonance frequency of 133 Cs is equal to 13.117 when B is 2.3488 T (a “100 MHz” magnet). Because the resonance/Larmor frequency is linearly dependent on B ( ν L = | γ /(2 π )| B = ω /(2 π ) ), then for a 133 Cs resonance frequency of 52.468, B =2.3488 × 52.468 / 13.117=9.3952 T (a “400 MHz” magnet). Thus: Δ E = μ z B = 7 γ ¡ B = 7 × 3.5339 × 10 7 rad/T/s × 6.626/2/ π × 10 − 34 Js × 9.3952 T = 2.45 × 10 − 25 J Δ E = μ Z B = γ ¡ B Δ E = μ Z B = 7 γ ¡ B Name _________________________ Exam 1, 2010: CHEM/BCMB 4190/6190/8189 2 2 ). At thermal equilibrium, the microscopic view of an ensemble of spins in a magnetic field can be illustrated by individual magnetic dipoles precessing about the axis corresponding to the magnetic field ( B ) direction ( z axis), as shown in the figure (panel A). Here M represents the macroscopic or bulk or net magnetization of the nuclear ensemble. a. Considering only the macroscopic, bulk magnetization vector M (i.e., panel B), draw a figure that shows the end result of application of a 180 degree electromagnetic pulse to the M shown in panel B. ( 2 points ) b. For spin ½ nuclei, the symbols N α and N β are used to represent the numbers of nuclei in the α and β states, respectively. Describe quantitatively the relationship between N α and N β in panel B above. Include in your description how the relationship between N α and N β contribute to M ....
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- Fall '08
- Magnetic Field, pulse, Nuclear magnetic resonance, degree pulse, total excitation bandwidth