Chemists use a wide array of techniques for determining the exact composition an

Question

Chemists use a wide array of techniques for determining the exact composition and structure of a compound. One of the most robust and interesting of these is nuclear magnetic resonance (NMR) spectroscopy. In this problem, you will see how NMR spectroscopy allows for the precise determination of the structure of an organic compound.

Nuclei with odd numbers of neutrons or protons have a magnetic moment. In the presence of a strong magnetic field, some nuclei will align parallel and some will align antiparallel to the field. If a sample is subjected to electromagnetic radiation with photon energy equal to the difference in energy between the two nuclear alignment states, some nuclei in parallel states will absorb a photon and flip to antiparallel states.

Suppose that a small shift ?f in the frequency of the absorbed radiation is observed. This shift is attributed to a small change ?? in the magnetic moment. What is the value of ???

Express your answer in terms of ?f, B, and h.

Explanation / Answer

Nucleus carries a positive charge. In some nuclei this charge spins on the nuclear axis and circulation of nuclear charge generates a magnetic dipole along the zixs. Thus the nucleus behaves like a tiny bar magnet having two poles.

The magnetic moment of the generated dipole is expressed in terms of nuclear magnetic moment () . Hence if an external magnetic filed is applied or the nucleus is placed in an external magnetic field then may have 2 possible orientations as follows ;

(1) In which the is aligned along the direction of external magnetic field B and is more stable(lower energy) ,alpha state.

(2) In which is aligned against the direction of the external magnetic field B and is less stable(high energy), beta state.

Hence at resonance there is a contineous balance between excitation and relaxation. This is called as nuclear magnetic resonance.

The energy required required for flipping the nucleus (proton) from its lower energy alignment to higher energy alignment depends upon the difference in energy (E = hv) . Hence how much energy is needed simply depends upon the strength of the external magnetic field which further depends upon the frequency of radiation to flip the spin

( frequency) v B (external magnetic filed)

v = (/2)* B

(Gyromagnetic ratio) = Magnetic moment / angular momentum = / L

   v = ( / L) * 2* B

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