BCH 330 Exam 3 questions with answers |\ |\ |\ |\ |\ |\
Describe how an NMR signal is generated within relaxed nuclear
|\ |\ |\ |\ |\ |\ |\ |\ |\ |\
spin, then excite and show what happens with time. Show how
|\ |\ |\ |\ |\ |\ |\ |\ |\ |\ |\
we get a peak from the raw data. - CORRECT ANSWERS ✔✔-to
|\ |\ |\ |\ |\ |\ |\ |\ |\ |\ |\ |\
initiate, one flips the nuclear magnetic vector by 90 degrees
|\ |\ |\ |\ |\ |\ |\ |\ |\ |\
using a radio frequency pulse
|\ |\ |\ |\
-result is the rotation about the z axis in the x-y plane
|\ |\ |\ |\ |\ |\ |\ |\ |\ |\ |\
-NMR signal is the result of relaxation back to being aligned with
|\ |\ |\ |\ |\ |\ |\ |\ |\ |\ |\ |\
bulk magnetic field while rotating around the z axis
|\ |\ |\ |\ |\ |\ |\ |\
-"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
|\ |\ |\ |\ |\ |\ |\ |\ |\
energy in time-space as magnetic vector relaxes
|\ |\ |\ |\ |\ |\
-3D relaxation processes have the form of attenuated period
|\ |\ |\ |\ |\ |\ |\ |\ |\
complex functions: spin evolves through space over time.
|\ |\ |\ |\ |\ |\ |\ |\
-chemical shift has units of parts per million (ppm) units,
|\ |\ |\ |\ |\ |\ |\ |\ |\ |\
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
|\ |\ |\ |\ |\ |\ |\ |\ |\ |\ |\
Guassian population |\
Show what a benzene ring does to the peak position (frequency)
|\ |\ |\ |\ |\ |\ |\ |\ |\ |\ |\
of H atoms at the periphery of atoms above the ring. Explain. -
|\ |\ |\ |\ |\ |\ |\ |\ |\ |\ |\ |\ |\
CORRECT ANSWERS ✔✔-nearby electrons affect the resonance
|\ |\ |\ |\ |\ |\ |\
frequency of the nuclear spin in an atom |\ |\ |\ |\ |\ |\ |\
,-for ex. , ring currents are produced by induction of pi electrons
|\ |\ |\ |\ |\ |\ |\ |\ |\ |\ |\ |\
circulating within double bonds and aromatic rings by the bulk
|\ |\ |\ |\ |\ |\ |\ |\ |\ |\
(Bo) field |\
-electronic perturbations can lead to large offsets in S values, e.g.
|\ |\ |\ |\ |\ |\ |\ |\ |\ |\
about 7 ppm downfield, "deshielded" in the spectrum of benzene
|\ |\ |\ |\ |\ |\ |\ |\ |\ |\
-the precise positioning of a proton with respect to two benzene
|\ |\ |\ |\ |\ |\ |\ |\ |\ |\ |\
rings leads to three different chemical shifts
|\ |\ |\ |\ |\ |\
-three different ring current environments produce three different
|\ |\ |\ |\ |\ |\ |\
chemical shifts
|\ |\
-In picture: the widespread S values in the pi alkane bridge-
|\ |\ |\ |\ |\ |\ |\ |\ |\ |\
containing benzene system |\ |\
--the precise position of the methylene protons leads to three
|\ |\ |\ |\ |\ |\ |\ |\ |\ |\
distinct chemical shifts |\ |\
Explain what a complex function is and what its complex
|\ |\ |\ |\ |\ |\ |\ |\ |\ |\
conjugate function is. - CORRECT ANSWERS ✔✔-imaginary |\ |\ |\ |\ |\ |\ |\
numbers often used in derivations and manipulations of
|\ |\ |\ |\ |\ |\ |\ |\
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
|\ |\ |\ |\ |\ |\ |\ |\ |\
magnitude, vectors with both magnitude and direction |\ |\ |\ |\ |\ |\
-relation to vectors involves the complex plane idea: the
|\ |\ |\ |\ |\ |\ |\ |\ |\
cartesian axis system version of this idea involves a real x axis
|\ |\ |\ |\ |\ |\ |\ |\ |\ |\ |\ |\
and an imaginary y axis
|\ |\ |\ |\
--polar coordinate version involves an axis system in which the
|\ |\ |\ |\ |\ |\ |\ |\ |\ |\
unit vector has length r and phase angle (theta) ranging from 0
|\ |\ |\ |\ |\ |\ |\ |\ |\ |\ |\ |\
to 2 pi (the standard unit circle setup in trigonometry)
|\ |\ |\ |\ |\ |\ |\ |\ |\
, -- length of polar coordinate vector r is calculated in terms of
|\ |\ |\ |\ |\ |\ |\ |\ |\ |\ |\ |\
cartesian coordinates: r=(x^2+y^2)^1/2 |\ |\
--phase angle (theta)=tan-1(y/x)|\ |\
--complex exponential is defined in terms of trigonometry
|\ |\ |\ |\ |\ |\ |\ |\
functions (exp)(z)=e^x (cosy+siny) e^z=e^2e^iy
|\ |\ |\
-cartesian to polar transformation function allows one to express
|\ |\ |\ |\ |\ |\ |\ |\ |\
the complex cartesian number z in the corresponding polar
|\ |\ |\ |\ |\ |\ |\ |\ |\
coordinate form" z=x+iy=re^(itheta) |\ |\
-complex variable (w) can always be converted to a real number
|\ |\ |\ |\ |\ |\ |\ |\ |\ |\ |\
by multiplying it by its complex conjugate (w*):
|\ |\ |\ |\ |\ |\ |\ |\
w+u+iv
w*=u-iv
ww*=u^2+v^2
Explain why these concepts are central to the interpretation of
|\ |\ |\ |\ |\ |\ |\ |\ |\ |\
quantum mechanics. - CORRECT ANSWERS ✔✔-target of many
|\ |\ |\ |\ |\ |\ |\ |\
quantum mechanics calculations, a wavefunction, only has
|\ |\ |\ |\ |\ |\ |\
physical meaning when multiplied by its complex conjugate (Y*)
|\ |\ |\ |\ |\ |\ |\ |\ |\
to produce Y^2
|\ |\
-according to Heisenburg, a key interpretation is that Y^2 is the
|\ |\ |\ |\ |\ |\ |\ |\ |\ |\ |\
probability of whatever one has calculated |\ |\ |\ |\ |\
-EX: quantities such as the electron distribution, coherance of a
|\ |\ |\ |\ |\ |\ |\ |\ |\ |\
spectroscopic signal, superimposed positions of x-rays diffracting |\ |\ |\ |\ |\ |\ |\
from a crystal |\ |\
-reality (Y^2) can be decomposed into two contributing
|\ |\ |\ |\ |\ |\ |\ |\
underlying sub-functions Y and Y*, which cannot be observed
|\ |\ |\ |\ |\ |\ |\ |\ |\
directly
Describe how an NMR signal is generated within relaxed nuclear
|\ |\ |\ |\ |\ |\ |\ |\ |\ |\
spin, then excite and show what happens with time. Show how
|\ |\ |\ |\ |\ |\ |\ |\ |\ |\ |\
we get a peak from the raw data. - CORRECT ANSWERS ✔✔-to
|\ |\ |\ |\ |\ |\ |\ |\ |\ |\ |\ |\
initiate, one flips the nuclear magnetic vector by 90 degrees
|\ |\ |\ |\ |\ |\ |\ |\ |\ |\
using a radio frequency pulse
|\ |\ |\ |\
-result is the rotation about the z axis in the x-y plane
|\ |\ |\ |\ |\ |\ |\ |\ |\ |\ |\
-NMR signal is the result of relaxation back to being aligned with
|\ |\ |\ |\ |\ |\ |\ |\ |\ |\ |\ |\
bulk magnetic field while rotating around the z axis
|\ |\ |\ |\ |\ |\ |\ |\
-"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
|\ |\ |\ |\ |\ |\ |\ |\ |\
energy in time-space as magnetic vector relaxes
|\ |\ |\ |\ |\ |\
-3D relaxation processes have the form of attenuated period
|\ |\ |\ |\ |\ |\ |\ |\ |\
complex functions: spin evolves through space over time.
|\ |\ |\ |\ |\ |\ |\ |\
-chemical shift has units of parts per million (ppm) units,
|\ |\ |\ |\ |\ |\ |\ |\ |\ |\
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
|\ |\ |\ |\ |\ |\ |\ |\ |\ |\ |\
Guassian population |\
Show what a benzene ring does to the peak position (frequency)
|\ |\ |\ |\ |\ |\ |\ |\ |\ |\ |\
of H atoms at the periphery of atoms above the ring. Explain. -
|\ |\ |\ |\ |\ |\ |\ |\ |\ |\ |\ |\ |\
CORRECT ANSWERS ✔✔-nearby electrons affect the resonance
|\ |\ |\ |\ |\ |\ |\
frequency of the nuclear spin in an atom |\ |\ |\ |\ |\ |\ |\
,-for ex. , ring currents are produced by induction of pi electrons
|\ |\ |\ |\ |\ |\ |\ |\ |\ |\ |\ |\
circulating within double bonds and aromatic rings by the bulk
|\ |\ |\ |\ |\ |\ |\ |\ |\ |\
(Bo) field |\
-electronic perturbations can lead to large offsets in S values, e.g.
|\ |\ |\ |\ |\ |\ |\ |\ |\ |\
about 7 ppm downfield, "deshielded" in the spectrum of benzene
|\ |\ |\ |\ |\ |\ |\ |\ |\ |\
-the precise positioning of a proton with respect to two benzene
|\ |\ |\ |\ |\ |\ |\ |\ |\ |\ |\
rings leads to three different chemical shifts
|\ |\ |\ |\ |\ |\
-three different ring current environments produce three different
|\ |\ |\ |\ |\ |\ |\
chemical shifts
|\ |\
-In picture: the widespread S values in the pi alkane bridge-
|\ |\ |\ |\ |\ |\ |\ |\ |\ |\
containing benzene system |\ |\
--the precise position of the methylene protons leads to three
|\ |\ |\ |\ |\ |\ |\ |\ |\ |\
distinct chemical shifts |\ |\
Explain what a complex function is and what its complex
|\ |\ |\ |\ |\ |\ |\ |\ |\ |\
conjugate function is. - CORRECT ANSWERS ✔✔-imaginary |\ |\ |\ |\ |\ |\ |\
numbers often used in derivations and manipulations of
|\ |\ |\ |\ |\ |\ |\ |\
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
|\ |\ |\ |\ |\ |\ |\ |\ |\
magnitude, vectors with both magnitude and direction |\ |\ |\ |\ |\ |\
-relation to vectors involves the complex plane idea: the
|\ |\ |\ |\ |\ |\ |\ |\ |\
cartesian axis system version of this idea involves a real x axis
|\ |\ |\ |\ |\ |\ |\ |\ |\ |\ |\ |\
and an imaginary y axis
|\ |\ |\ |\
--polar coordinate version involves an axis system in which the
|\ |\ |\ |\ |\ |\ |\ |\ |\ |\
unit vector has length r and phase angle (theta) ranging from 0
|\ |\ |\ |\ |\ |\ |\ |\ |\ |\ |\ |\
to 2 pi (the standard unit circle setup in trigonometry)
|\ |\ |\ |\ |\ |\ |\ |\ |\
, -- length of polar coordinate vector r is calculated in terms of
|\ |\ |\ |\ |\ |\ |\ |\ |\ |\ |\ |\
cartesian coordinates: r=(x^2+y^2)^1/2 |\ |\
--phase angle (theta)=tan-1(y/x)|\ |\
--complex exponential is defined in terms of trigonometry
|\ |\ |\ |\ |\ |\ |\ |\
functions (exp)(z)=e^x (cosy+siny) e^z=e^2e^iy
|\ |\ |\
-cartesian to polar transformation function allows one to express
|\ |\ |\ |\ |\ |\ |\ |\ |\
the complex cartesian number z in the corresponding polar
|\ |\ |\ |\ |\ |\ |\ |\ |\
coordinate form" z=x+iy=re^(itheta) |\ |\
-complex variable (w) can always be converted to a real number
|\ |\ |\ |\ |\ |\ |\ |\ |\ |\ |\
by multiplying it by its complex conjugate (w*):
|\ |\ |\ |\ |\ |\ |\ |\
w+u+iv
w*=u-iv
ww*=u^2+v^2
Explain why these concepts are central to the interpretation of
|\ |\ |\ |\ |\ |\ |\ |\ |\ |\
quantum mechanics. - CORRECT ANSWERS ✔✔-target of many
|\ |\ |\ |\ |\ |\ |\ |\
quantum mechanics calculations, a wavefunction, only has
|\ |\ |\ |\ |\ |\ |\
physical meaning when multiplied by its complex conjugate (Y*)
|\ |\ |\ |\ |\ |\ |\ |\ |\
to produce Y^2
|\ |\
-according to Heisenburg, a key interpretation is that Y^2 is the
|\ |\ |\ |\ |\ |\ |\ |\ |\ |\ |\
probability of whatever one has calculated |\ |\ |\ |\ |\
-EX: quantities such as the electron distribution, coherance of a
|\ |\ |\ |\ |\ |\ |\ |\ |\ |\
spectroscopic signal, superimposed positions of x-rays diffracting |\ |\ |\ |\ |\ |\ |\
from a crystal |\ |\
-reality (Y^2) can be decomposed into two contributing
|\ |\ |\ |\ |\ |\ |\ |\
underlying sub-functions Y and Y*, which cannot be observed
|\ |\ |\ |\ |\ |\ |\ |\ |\
directly
