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How many spin states does 14N (I=1) have?

Number of nuclear spin states = 2I + 1

A/Z odd, I = integer
A/Z even, I = 0
A/Z even/odd or odd/even, I = half integer


Explain why stronger external magnetic fields result in larger ΔE between the spin states

Atoms have intrinsic spin that is a result of their quantum mechanical properties. The spin quantum number of a nucleus, I, determines the number of allowed spin states, 2I+1. These spin states each assume a different orientation when interacting with an external magnetic field. The orientations of the spin states change the relative magnetic moments of each spin state by a constant (determined by quantum mechanics) amount. Because of this, increasing field strength, B0, proportionally increases ∆E.


Is NMR more or less sensitive than IR? Explain.

NMR is not very sensitive, for a few reasons:
The proportion of protons contributing to the net magnetic dipole moment aligned with the field is very low (around 4 per million @ room temp), so the relative amount of sample must be high.
This low net number of atoms in the lower energy state means that the experiment may become saturated quickly, as only those contributing to the net moment are measurable.
This can be increased through multiple acquisitions (increase S/N by sqrt of the number of runs), increasing strength of external magnetic field (+∆E), using H1 for higher natural abundance or being sure to properly grow your sample saturated with the correct isotope, using partial spin flipping.


How many Hz is 1 ppm for 1H on a 700 MHz instrument?

1 ppm = 700MHz/10^6 = 700 Hz


In equilibrium, what is the net magnetization in the x-plane? Explain.

The net magnetisation in the x-plane is 0. The applied field (B0) is along the z-axis, and while there will be some components of magnetisation in the x-plane, their directions are random and will cancel each other out producing no net moment.


What is the effect of a 90 degree pulse applied along the -x-axis on the total M0 magnetisation?

The magnitude of M0 does not change, but the net magnetisation will rotate into the transverse plane to the +y-axis.


What is the frequency of the B1 oscillating field (pulse)?

The Larmor frequency, the rotating reference frame


Which variables allow control of the resulting angle (θ) of a pulse?

The time of the pulse and strength of the field
Θ=γ B1 tp (/2pi for rad s-1)


Why is the advantage of the Fourier Transform?

It allows you to see specific frequencies plotted as relative intensities, it translates the time domain into the frequency domain and demultiplexes it.


Why do the amide protons in a protein give larger chemical shifts than the methyl protons?

The amide protons are more de-shielded, that is there is less electron density surrounding the amide protons with which to counteract (through induction) the force of the applied magnetic field. Stronger magnetic field gives a higher frequency (higher shift).


How does hydrogen bonding affect the chemical shift of the proton?

The proton is shifted downfield from the unbonded protein, due to a decrease of electron density because of the bond


Why does a short-lived NMR signal result in peak broadening?

T2 is the relaxation time, the time it takes for the component of M0 in transverse plane to decay to 0. The full width half maximum (width of the peak measured at ½ height) is proportional to 1/πT2, so shorter NMR signals (with shorter T2) will have wider peaks. Because the integral of the peak is proportional to the signal strength of the peak, this will lower the peak height as well, increasing perception of the effect.


The flexible regions of a protein give higher signal than the rigid ones. Why? (Hint:relaxation properties)

T2 is proportional to the mobility of atoms. Atoms in the rigid portions of the protein experience more static fields than those in freeer movement, decreasing T2. Additionally, spectral density J(ω) decreases at the Larmor frequency for slower moving atoms.


A single NMR scan of a sample has a S/N ratio of 2.4. If each scan requires 4 sec, what is the minimum time required to obtain a spectrum with a S/N ratio of 7.2?

S/N increases with the square root of the number of scans.
1 scan = 2.4
7.2/2.4 = 3
3^2 = 9 scans * 4s/scan = 36s


Does the sensitivity of the experiment increase, decrease or stay the same when:
(i) the strength of the magnet is increased
(ii) the temperature of the sample is increased
(iii) 2H was observed instead of 1H
(iv) a sample of 10 mm diameter is used instead of 5 mm
(v) The concentration of the sample is increased.

S/N = n γe sqrt(γd^3 B0^3 t)
where n is your net Boltzman distribution (e^∆E/kT) of observable spins (i.e., concentration), γe is the gamma of what your exciting (for proton it's 42.576 MHz per Tesla of your magnet), sqrt is the square root, γd is the gamma of what you're detecting, Bo is the field strength of your magnet, and t is the total acquisition time (i.e., number of scans).

i) Sensitivity increases exponentially as the strength of the magnetic field is increased, due to both larger B0 and larger ∆E
ii) Sensitivity decreases with increasing temperature
iii) The gyromagnetic ratio of deuterium is much smaller than that of hydrogen, so the S/N will decrase
iv) Increase, the coil area is larger so more sample (molecules) can fit into the field
v) Increase, although the Boltzmann constant has not changed, there will be more nuclei in the α state just due to increased numbers


Assume a mixture of DMSO in water. The T1 relaxation value is 2 sec for DMSO and 4 sec for water. (a) Explain how you can use the inversion-recovery pulse sequence to suppress or eliminate the signal of water while observing the signal from DMSO. (b) For what τ value is the water signal completely suppressed and what is the loss in the intensity of the DMSO signal in this case?

(a) Inversion recovery uses an initial 180° pulse that reverses the longitudinal magnetisation (M0) towards the negative z-axis. As the longitudinal vector relaxes towards the positive z-axis, nuclei from different environments will experience net zero longitudinal magnetisation (Mz) at different time intervals corresponding to T1. Spin-echo signals generated when nuclei are close to Mz=0 will produce little or no signal and make no significant contribution to the image.
(b) TInull=T1[ln2 – ln(1 + e-TR/T1)], when TR>>T1 reduces to T1(ln2) ≈ 0.69•T1