J.J. Thomson proposed a model of the atom known as the "plum pudding" model. In this model, Thomson suggested that atoms consist of a positively charged sphere in which electrons are embedded, similar to seeds in a watermelon. This model attempted to explain the electrical neutrality of atoms and how negative and positive charges were distributed within an atom.

Let's explore the reasoning behind the correct option and eliminate the incorrect ones:

1. Randomly placed inside the nucleus: This option is incorrect. According to modern atomic models, electrons are found outside the nucleus in defined orbitals and not inside it. The nucleus contains protons and neutrons.
2. Embedded in a positively charged sphere like seeds in a watermelon: This is the correct representation of Thomson's model. Electrons are embedded within a positively charged "soup," maintaining the atom's neutrality.
3. Moving in fixed orbits around the nucleus: This describes the Bohr model, which came after Thomson's model. In Bohr's model, electrons move in fixed orbits at certain energy levels around the nucleus.
4. Orbiting around neutrons in elliptical paths: This option is incorrect, as neutrons were discovered much later and do not influence electron configurations in early atomic models like Thomson's.

In conclusion, Thomson's model describes the electrons as being embedded in a positively charged sphere, akin to seeds in a watermelon, signifying an even distribution of positive charge with negatively charged electrons. Although it couldn't explain all experimental results, it was an important step in the development of atomic theory.