State the limitations of the plum pudding model of the atom.

(N/A) The plum pudding model,proposed by $J.J. Thomson$,has several significant limitations:
$1$. According to the laws of electrostatics,a stable distribution of stationary charges is not possible. The electrons within the atom experience a $Coulomb$ force due to the positive charge distribution. Consequently,they cannot remain stationary and would move with acceleration,making the atom unstable.
$2$. The model fails to explain the origin of atomic spectra. Every condensed matter at any temperature emits electromagnetic radiation with a continuous distribution of wavelengths. In contrast,rarefied gases heated in a flame emit light with only discrete wavelengths,appearing as a series of bright lines.
$3$. In such gases,the average spacing between atoms is large,implying that the radiation is emitted by individual atoms rather than through interactions between them. This suggests an intimate relationship between the internal structure of an atom and its radiation spectrum,which the plum pudding model could not account for.