Question

why does nuclear over hauser effect do not produce large increase in intensity for hydrogen when carbons are irradiated

Answer 1

The degree of the signal enhancement is called the nuclear overhauser enhancement and is hetero nuclear effect. It appears generally when one of two types of atoms is irradiated, while the spectrum of the other is observed. In case of hydrogen irradiated 13C is observed with intense peak here proton -coupled spectrum is proportional to the number of protons attached and the effect can be positive or negative.

But in case of carbon irradiated 1H is observed will the very less intensity it is because due to the low prevalence of 13C and it is because NOE for 13C-1H operates in the opposite direction which means a rare nuclei always bound to the abundant one.

And also NOE effect is very short ranged as it is 1/r^{​​​​​​3}​​​​​ the distance between the nuclei.