9 According to eq. 2-8, this frequency depends only on the magnetic field strength Bo and the spin,s gyromagnetic ratio y. For a field strength of 11.7 T one finds the following resonance frequencies for the most important isotopes Isotope y(relative) resonance fre relative quency at 11.7T abundance sensitivity 500 MHZ 9998% 25 125 MHZ 1.1% 50 MHZ 0.37% 455 MHZ 100% 0.8 99 MHZ 4.7% P 40 203 MHZ 100% 0.07 also taking into account typical linewidths and relaxation rates △E=?hB The energy difference is proportional to the bo field strength B c How much energy can be absorbed by a large ensemble of spins (like our NMR sample)depends on the population difference between the a and B state(with equal population, rf irradiation same number of spins to absorb and emit energy: no net effect observable!) According to the boltzmann equation N(csexp I=exp 2kT △E N(B) For 2.35 T(=100 MHz) and 300 K one gets for H a population difference N(a)-N(B)of ca. 8. 10-6 i.e., less than /1000 of the total number of spins in the sample!9 According to eq. 2-8, this frequency depends only on the magnetic field strength B0 and the spin's gyromagnetic ratio g. For a field strength of 11.7 T one finds the following resonance frequencies for the most important isotopes: Isotope g (relative) resonance fre￾quency at 11.7 T natural abundance relative sensitivity* 1H 100 500 MHz 99.98 % 1 13C 25 125 MHz 1.1 % 10-5 15 N -10 50 MHz 0.37 % 10-7 19 F 94 455 MHz 100 % 0.8 29 Si -20 99 MHz 4.7 % 10-3 31 P 40 203 MHz 100 % 0.07 · also taking into account typical linewidths and relaxation rates The energy difference is proportional to the B0 field strength: How much energy can be absorbed by a large ensemble of spins (like our NMR sample) depends on the population difference between the a and b state (with equal population, rf irradiation causes the same number of spins to absorb and emit energy: no net effect observable!). According to the BOLTZMANN equation N N E kt hB kT ( ) ( ) exp exp a b g p = = D 0 2 [2-9] For 2.35 T (= 100 MHz) and 300 K one gets for 1H a population difference N(a)-N(b) of ca. 8.10-6, i.e., less than 1 /1000 % of the total number of spins in the sample!