Question

Why is the number of absorbing protons proportional to the area under a `""^1 "H"` NMR signal?

Answer 1

`""^1 "H"` NMR detects responses to an external magnetic field, targeting specifically proton environments; the more protons in the environment, the greater the responses detected, the more intense the signal, and the larger the area under the peak.

Basically, since the nuclei of each proton is identical (no regular proton is different from another one), the responses acquired from detecting each of their behaviors in a magnetic field are identical.

Therefore, they each contribute the same relative amount to the overall peak area. In other words, the number of absorbing protons is therefore proportional to the area under the peak.