In NMR spectroscopy is a constant field of radio waves applied while the external magnetic field is gradually changed from low to high or is it the other way around? I suppose you could do it either way but I'm wondering what the convention is because I don't know which one they are talking about in my book since the diagrams just have "Chemical shift" in ppm as the x axis and "Intensity" as the y axis.
I was asking one of my chemistry friends about this the other day, but she really didn't know much about the physics. To me it seems sensible that the positive direction on the horizontal axis would indicate an upwards shift in the resonant frequency, if you had instead kept the magnetic field constant and swept the RF field. The energy difference between the nuclear spin states is proportional to the magnetic field strength, so the resonant frequency will be too... Ok so I think that means if you hold the light frequency constant and move the field, as you increase the field you will bring the lower energy peaks into resonance one at a time, in the order inverse to their energy, so that a graph of I vs f will have the peak order around the opposite way to I vs B. Ok sorry, doesn't really help figure out which was is most sensible, seems to me the ppm shift could be mean either of your options, depending on whether you prefer to think of the resonant frequency shifting or the field strength where the resonance is found shifting. I don't actually do chemistry so I'm not sure what they think.
In any modern NMR the field is kept constant and the radio pulse contains a wide spectrum of frequencies. Many years ago, when wide-spectrum radio sources were hard to make and NMR magnets were simply electromagnets, it was the other way around.
I am too lazy to search but based on 50 year old understanding I think each pulse of RF is a well defined frequency, which in a uniform B field will resonately add energy only to certain energy level or better stated make some set of nuclear spins all precess/ oscillate in phase. The RF field will add and then subtract energy to & from the non-resonate spins and definitely not get them into mutual in phase oscillation. When the driving RF pulse is turned off, only these "in phase" spins will give significant radiant energy back to the receiver of the NMR set. Their "echo" will rapidly die out as they lose phase with each other, but "hearing" that echo tells you that the well defined frequency of that RF pulse did excite reasonately some set of nuclei. Thus, I don't think any one RF pulse has a broad spectrum, but an RF source capable of sequentially producing a wide spectrum of frequencies via electronic control is desirable. Long ago, one changed the RF frequency by manually tuning the transmitter/source. Then it may have been better to use a fixed frequency RF pulses and slowly sweep the B field intensity. Note that lets the receiver always be listening for only one frequency of echo. Again I note this is all from memory of 50 year old information. Back then NMR was mainly used by chemists to explore atomic structure of molecules. Medical applications came later, along with a new name (Magnetic Resonance Imaging, MRI, to avoid the "scary" word nuclear). The reason chemist could get information about the electronic configuration is that the quantized nuclear spin precession levels do ever so slightly depend upon the electronic configurations around the nucleus. The radiation somehow comes for the nuclear spin changing levels. I think the spacing between the quantized levels are essentially the same so each step down gives out the same packet of energy. There is probably a good bit wrong here in detail, but I think the spirit is correct - my point with this post was to explain why I think each RF pulse is one frequency, not a band of frequencies.
continuous wave and fourier transform If I recall correctly, in the early days of NMR, the radio wave frequency applied was kept constant but the magnetic field was changed gradually. The problem with this was that the nuclei were excited one-by-one. I don't really know why it is necessary to excite all the nuclei at the same time but I suppose this is required for more advanced applications. The old way of doing it was called "Continuous Wave Spectroscopy". The modern way of doing NMR spectroscopy is to keep the magnetic field constant (very finicky! slight deviations in magnet temperature can result in variable magnetic field strengths). A short pulse of RF energy of many frequencies was then applied. The signal recorded (it's like a sine wave with varying amplitudes) is called the FID or free induction decay, if I remember correctly. This FID contains information from all the relaxing species combined into one humongous and complicated sine wave. To ascertain the resonant frequencies, a fourier transform is applied to give you a frequency-intensity spectra. In the good old days, Fourier transforms were hard to apply due to computational limitations. But with the advent of computers and fast fourier transform algorithms, this became a reality. Thus, most modern NMR spectrometers are referred to as "FT-NMR" spectrometers for fourier transform NMR spectrometers. The chemical shift comes from the fact that the resonant frequency of a nucleus under a given magnetic field strength will vary SLIGHTLY. This slight variation is the subject of most NMR experiments. TO measure this slight variability, you need a reference. For 1H, 13C and 29Si, the standard used is tetramethysilane. The frequency is then set to zero. To get the chemical shifts of the nuclei in your sample, you have to subtract the reference frequency from the obtained frequency. THen you divide this difference by the operating frequency of the magnet. This is because the operating frequency varies with magnetic field strength. Since it's frequency divided frequency, the chemical shift is unitless. And since the difference is very small (operating frequency is in MHz and resonant frequencies in Hz), it's reported in parts per million.
Welcome to Sciforums eddanco. That seems very reasonable - getting all the data at once instead one echo at a time. Probable the old way was necessary in part for signal to noise ratio problems. I.e. one put all the RF power in at one frequency. Now with better receivers, one can hit the sample with a broad spectrum of RF, record the broad spectrum echo and then with some Fast Fourier transform get the relative strength at each frequency in a few minutes, not hours, even though each was excited with much less power. The point you (and I) made that the electronic configuration only very slightly shift the frequencies is important and yes a tiny variation in the B field kills the system.
The duration of the pulse is kept very short, and thanks to the uncertainty principle it's able to excite across a broad range of frequencies.
I don't think the "uncertainty principle" has anything to do with there being a wide frequency content in very short pulse. That is a simple Fourier fact. For example, lightning strokes are very broad spectrum RF sources. Certain frequencies they produce use the ionosphere and Earth surface as a waveguide so with that RF you can hear them anywhere they strike on Earth.
The uncertainty of the RF pulse's wavelength is equal to Dirac's constant over the pulse duration. If the pulse duration is small, the uncertainty is large enough to let the pulse excite across the entire range of wavelengths needed.
Plug some numbers in and see how short the pulse would need to be for the energy of the pulse to be quantumically uncertain by even a factor or 2. I.e. highest frequency (energy) three times that of the lowest. I bet the period of pulse, QM's "delta t", needs to less than a pico-second to make QM's "delta E" = E where E is the mean of the spread. For example if the lowest frequency (or energy) is f and the highest is F where F = 3f then the mean is 2f so the spread is 3f-1f = 2f which is the mean or sort of then nominal RF frequency. Maxwell, and I think Hertz, knew that the first RF ever made, a spark gap pulse, had a wide frequency spread as he knew Fourier theory (and neither had never heard of QM or the uncertainty principle).
The energy differences between the excitation frequencies of the different nuclei are very tiny, much less than a factor of 2. When taking a proton spectrum in a typical NMR spectrometer with a 7 Tesla magnet, you would scan over a range of about 300.000 MHz to 300.003 MHz. The pulse times vary greatly depending on what kind of experiment you want to do, but usually start in the low microseconds and increase from there. Note that if you look on the bottom of pretty much any NMR spectra you'll see that the x axis is in units of "ppm," which is parts per million variation in the frequency...which is not much energy difference. Edit: I assume that when you ask about a factor of two for the energy uncertainty, you're asking about the frequency range that NMR spectrometers typically operate in. Otherwise the question would be impossible to answer, since it would depend on the initial frequency...
Yes as I explained and eddanco stated, the energy shift (or range of frequencies the echo will be found in) by the electronic environment of the nucleus is very tiny but enough to tell something about that electronic environment to the research chemist. Yes for the proton spin (there are others of interest) your 3KHz spread is due to the short pulse duration as nay Fourier analysis will show. Again my point is only that quantum mechanic's uncertainty principle has nothing to due with making the 3KHz spread. No, not at all. I was trying to show was that an extremely brief RF pulse duration period (less than a pico-second as "delta t") is required in the QM uncertainty product (delta t)(delta e) to give much spread in delta e (or in this case as e and frequency are directly proportional in delta f, the frequency spread. What I was saying, both about Fourier and the QM uncertainty, is valid and we need not be speaking of NMR at all. In fact I mentioned lightning strikes brief period causing, and shown by Fourier analysis, a wide RF spectrum. There too QM's uncertainty principle has nothing to do with making the spread of frequencies produced by lightning's short duration of the individual "strikes" in the typical "bolt"
I don't follow you, Billy T. How exactly does a Fourier analysis show that the 3 KHz spread is due to the short pulse time? A Fourier analysis will allow you to break the pulse down into the various frequency-domain waves that make up the pulse, but I don't understand what you think the pulse duration has to do with that. Or perhaps when you say "Fourier analysis" you mean something other than changing the radio signal from the time domain to the frequency domain? In any case, I have multiple textbooks on NMR that explicitly state that the ability of the radio pulse to excite across the necessary range of wavelengths is due to the short pulse duration and subsequent application of the uncertainty principle to the pulse wavelength. I guess it depends on what you mean by "much spread." For the purposes of NMR, the microsecond pulse times that are commonly used are more than sufficient to create the necessary spread and knock all the relevant nuclei into a different angle of precession. I don't have any idea what the duration of a lightning strike is, but if it's sufficiently short, then the uncertainty principle will indeed play a role in determining the spread of its RF emissions.
If you do the Fourier analysis on a 1000 cycles of a pure sin wave and compare that to the analysis on a 100 cycles of the same sine wave you will find that the frequency content of the shorter pulse of a truncated perfect sine wave is wider. I admit that I am too lazy to actually calculate by Fourier analysis how many cycles of a truncated, but other wise pure 300Mhx sine wave has 3Khz spread of frequencies as it frequency content. Likewise I have not used the QM uncertainty equation's value for the product of (delta T)(delta E) to see what an energy E uncertainty corresponding to 3Khz implies for the delta T = the duration of the pulse would be. Perhaps I am wrong and the spread of 3KHz can be due to the uncertainty principle, but that (delta T)(delta E) product is very tiny and, I think the delta E corresponding to 3Khz is very large, forcing the Delta T to be very small. I guessed sub pico-second duration for the Delta T factor in the uncertainty product.
Well, if you're going to force me to do math... 3000 Hz = 1.24*10^-11 eV deltaT = dirac's constant/delta E = 6.58*10^-16 eV S/1.24*10^-11 eV = 5.3*10^-5 seconds, or 53 microseconds. Actual pulse times are usually around 5-10 microseconds, far shorter than is needed to give a 3 KHz spread.
Thanks. I checked your values as the result surprizes me, but you are correct and my guess badly wrong. Thanks for correcting me. I think I was too influence by years of experience with visible light energy in eV. - Did not realize by guess how much smaller 3kHz is.
No problem, I'm just glad there was finally some discussion in the chemistry forum... Anyway, the very subtle energy differences involved illustrates why you need such strong magnetic fields. The relaxation times of the nuclei in an NMR experiment are on the order of microseconds, so when you're talking about peak separations that are measured in just hundreds of Hz or less, the uncertainty from the short excited state lifetime causes very significant line broadening that can ruin your spectra.
