BCH 330 Exam 3 questions with answers

BCH 330 Exam 3 questions with answers |\ |\ |\ |\ |\ |\




Describe how an NMR signal is generated within relaxed nuclear
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spin, then excite and show what happens with time. Show how
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we get a peak from the raw data. - CORRECT ANSWERS ✔✔-to
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initiate, one flips the nuclear magnetic vector by 90 degrees
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using a radio frequency pulse
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-result is the rotation about the z axis in the x-y plane
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-NMR signal is the result of relaxation back to being aligned with
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bulk magnetic field while rotating around the z axis
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-"right-hand rule" from electromagnetism requires that the |\ |\ |\ |\ |\ |\ |\


relaxation pathway follow a chiral corkscrew-like route |\ |\ |\ |\ |\ |\




-magnetic field rotation direction rule leads to conservation of
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energy in time-space as magnetic vector relaxes
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-3D relaxation processes have the form of attenuated period
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complex functions: spin evolves through space over time.
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-chemical shift has units of parts per million (ppm) units,
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calculated relative to the frequency of a suitable internal |\ |\ |\ |\ |\ |\ |\ |\ |\


standard
-individual spin sub-components correspond to frequencies that |\ |\ |\ |\ |\ |\ |\


are larger and smaller than the central peak component in the
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Guassian population |\




Show what a benzene ring does to the peak position (frequency)
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of H atoms at the periphery of atoms above the ring. Explain. -
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CORRECT ANSWERS ✔✔-nearby electrons affect the resonance
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frequency of the nuclear spin in an atom |\ |\ |\ |\ |\ |\ |\

,-for ex. , ring currents are produced by induction of pi electrons
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circulating within double bonds and aromatic rings by the bulk
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(Bo) field |\




-electronic perturbations can lead to large offsets in S values, e.g.
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about 7 ppm downfield, "deshielded" in the spectrum of benzene
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-the precise positioning of a proton with respect to two benzene
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rings leads to three different chemical shifts
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-three different ring current environments produce three different
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chemical shifts
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-In picture: the widespread S values in the pi alkane bridge-
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containing benzene system |\ |\




--the precise position of the methylene protons leads to three
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distinct chemical shifts |\ |\




Explain what a complex function is and what its complex
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conjugate function is. - CORRECT ANSWERS ✔✔-imaginary |\ |\ |\ |\ |\ |\ |\


numbers often used in derivations and manipulations of
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equations containing vectors |\ |\




-complex numbers are written in the form: z=x+iy. |\ |\ |\ |\ |\ |\ |\ |\




--imaginary root i=(-1)^1/2 |\ |\




-numbers are divided into scalars and vectors: scalars with
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magnitude, vectors with both magnitude and direction |\ |\ |\ |\ |\ |\




-relation to vectors involves the complex plane idea: the
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cartesian axis system version of this idea involves a real x axis
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and an imaginary y axis
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--polar coordinate version involves an axis system in which the
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unit vector has length r and phase angle (theta) ranging from 0
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to 2 pi (the standard unit circle setup in trigonometry)
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, -- length of polar coordinate vector r is calculated in terms of
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cartesian coordinates: r=(x^2+y^2)^1/2 |\ |\




--phase angle (theta)=tan-1(y/x)|\ |\




--complex exponential is defined in terms of trigonometry
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functions (exp)(z)=e^x (cosy+siny) e^z=e^2e^iy
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-cartesian to polar transformation function allows one to express
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the complex cartesian number z in the corresponding polar
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coordinate form" z=x+iy=re^(itheta) |\ |\




-complex variable (w) can always be converted to a real number
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by multiplying it by its complex conjugate (w*):
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w+u+iv
w*=u-iv
ww*=u^2+v^2


Explain why these concepts are central to the interpretation of
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quantum mechanics. - CORRECT ANSWERS ✔✔-target of many
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quantum mechanics calculations, a wavefunction, only has
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physical meaning when multiplied by its complex conjugate (Y*)
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to produce Y^2
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-according to Heisenburg, a key interpretation is that Y^2 is the
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probability of whatever one has calculated |\ |\ |\ |\ |\




-EX: quantities such as the electron distribution, coherance of a
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spectroscopic signal, superimposed positions of x-rays diffracting |\ |\ |\ |\ |\ |\ |\


from a crystal |\ |\




-reality (Y^2) can be decomposed into two contributing
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underlying sub-functions Y and Y*, which cannot be observed
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directly