The correct answer is option 1, Dalton. Dalton proposed the theory that the atom is indivisible. This theory, known as Dalton`s atomic theory, was put forth in the early 19th century. According to Dalton, atoms are the building blocks of matter and cannot be divided further. He believed that all substances consisted of small, indivisible particles called atoms, which combine to form compounds through chemical reactions.

Option 2, Berzelius, is incorrect. While Berzelius made significant contributions to the field of chemistry, he did not propose that the atom is indivisible.

Option 3, Rutherford, is also incorrect. Rutherford is renowned for his gold foil experiment, which led to the discovery of the atomic nucleus. He determined that the atom has a positively charged nucleus at its center, but he did not propose that the atom is indivisible.

Option 4, Avogadro, is unrelated to the concept of the atom being indivisible. Avogadro is known for Avogadro`s law, which relates the volume and number of moles of a gas.