In the present study, the impurity binding energy (IBE) and the normalized IBE (NIBE) of GaAs quantum dot (QD) are meticulously scrutinized. The QD contains Gaussian impurity as dopant. Gaussian white noise, applied via two different routes (additive and multiplicative), also becomes part of the QD confinement potential. The IBE and NIBE exhibit (depending on presence/absence of noise, mode of entrance of noise and the given physical parameter undergoing change) steady growth, steady fall, and maximization. Over the whole study, the NIBE plots efficiently manifest some intricate features which IBE plots fail to do and establish their greater efficacy over the IBE plots in unveiling the influences of various physical parameters. The findings of the study appear to be quite pertinent in realizing the optical properties of low‐dimensional nanostructures containing impurity and under the aegis of noise.