Nuclear magnetic resonance (NMR) is a physical phenomenon based upon the quantum mechanical magnetic properties of an atom's nucleus. All nuclei that contain odd numbers of protons or neutrons have an intrinsic magnetic moment and angular momentum. The most commonly measured nuclei are 1 H (the most receptive isotope at natural abundance) and 13 C, although nuclei from isotopes of many other elements (in our measurement 19 F) can also be observed. NMR resonant frequencies for a particular substance are directly proportional to the strength of the applied magnetic field, in accordance with the equation for the Larmor precession frequency. Because Larmor precession is typical, we can recognize what particles we are studying. And that is what NMR is about. NMR apparatus Theory Measurement and results After we have understood the principles of NMR and made the apparatus work, we made 2 experiments. The first one (g factor measurement) was from the instruction sheet. We thought up the second one, quantity of hydrogen in a sample. We used a set of devices for NMR from Leybold instruments inc. But we needed also some other devices: teslameter ampermeter stable power supply (the original one was fluctating) digital oscilloscope Tektronix DPO 4054 (we used digital one because it allowed us to analyze the data in a computer) If a nucleus is placed in a magnetic field, the interaction between the nuclear magnetic moment and the external magnetic field means the two states no longer have the same energy. The energy of a magnetic moment μ when in a magnetic field B 0 (the zero subscript is used to distinguish this magnetic field from any other applied field) is given by the negative scalar product of the vectors: where the magnetic field has been oriented along the z axis. It follows: As a result the different nuclear spin states have different energies in a non-zero magnetic field. In hand-waving terms, we can talk about the two spin states of a spin ½ as being aligned either with or against the magnetic field. If γ is positive (true for most isotopes) then m = ½ is the lower energy state. The energy difference between the two states is and this difference results in a small population bias toward the lower energy state. Resonance Resonant absorption will occur when electromagnetic radiation of the correct frequency to match this energy difference is applied. The energy of a photon is E = hf, where f is its frequency. Hence absorption will occur when These frequencies typically correspond to the radio frequency range of the electromagnetic spectrum. It is this resonant absorption that is detected in NMR. G factor measurementQuantity of hydrogen in a sample G factor is a number typical for every nucleus. It is the proportion of magnetic field and Larmor frequency in these the resonation of the sample happens. We know the exact value of the frequency, because the oscillator creates it. But the value of magnetic field is measured only indirectly from the value of electric current in the coils. The dependence of magnetic field on electric current cannot be easily counted so we had to measure behavior of magnetic field as a function of the electric current and then fit this to a function. From this function we were then probing what magnetic field is applied on the sample. By measurement we had a little problem with hysteresis but we avoided it later. Then we measured electric current flow trought the sensing coil at selected frequencies and calculated the g-factor from obtained current values. SampleResultsTable results Glycerin (hydrogen) 5,765,59 PTFE (fluor)5,445,25 Introduction With hysteresis First, not very exact measuerement Without hysteresis We measure resonance of the nuclei of the same element in the same magnetic field and at the same temperature. The area of the signal directly proportional to the quantity of the element in the sample. This way we can discover quantity of an element in the sample if we know the quantity of the same element in other sample. We knew quantity of hydrogen in the distilled water, so we were able to measure the quantity of hydrogen in any other sample that fits to the measuring tube. To be able to count the area of the signal (red) we needed to fit it to a function (green). Then we integrated it and we got these results: Resonance signal of distilled water SampleAreaQuantity H [%] Water0, % Banana0, % Apple0, % We were surprised by the result because we thought that there is more hydrogen in water then in banana or apple. We think it is because there is much more hydrogen in long and complicated carbohydrates. PTFE resonance Banana This experiment is a part of project Cesta k Vědě, that is supported by European Union and by Prague municipal authority, it was made by two students from Gymnázium Jaroslava Seiferta, Jan Kubant and Tomáš Přeučil. But we could not make it without help of our tutors, Ing. David Tlustý and Ing. Michal Petráň.