Śrīla Prabhupāda Says - [Regarding how the jīva (soul) is smaller than even the atom]

The sage does not make any distinction on the basis of color, intelligence, or species. He sees every living entity as a small particle of spirit soul. It is stated:

keśāgra-śata-bhāgasya
śatāṁśaḥ sādṛśātmakaḥ
jīvaḥ sūkṣma-svarūpo "yam
saṅkhyātīto hi cit-kaṇaḥ
[Cc. Madhya 19.140]

"There are innumerable particles of spiritual atoms, which are measured as one ten-thousandth of the upper portion of a hair."

Because we have no instrument to measure the dimensions of the spirit soul, the small particle of spirit soul is measured in this way. In other words, the soul is so small that it is smaller than an atom. That small particle is within you, within me, within the elephant, within gigantic animals, in all men, in the ant, in the tree, everywhere. However, scientific knowledge cannot estimate the dimensions of the soul, nor can a doctor locate the soul within the body.

Consequently material scientists conclude that there is no soul, but that is not a fact. There is a soul. The presence of the soul makes a difference between a living body and a dead body. As soon as the soul departs from the body, the body dies. It has no value. However great a scientist or a philosopher one may be, he must admit that as soon as the soul departs from the body, the body dies. It then has no value and has to be thrown away. We should try to understand this; the soul is valuable, not the body. The fact that the soul is transmigrating is explained in the Bhagavad-gītā (2.22):

vāsāṁsi jīrṇāni yathā vihāya
navāni gṛhṇāti naro "parāṇi
tathā śarīrāṇi vihāya jīrṇāny
anyāni saṁyāti navāni dehi

"As a person puts on new garments, giving up old ones, similarly, the soul accepts new material bodies, giving up the old and useless ones."

When a suit becomes old, we give it up and accept another suit; similarly the soul is changing dresses according to desire. Because the soul is part and parcel of God, it has godly qualities. God is the supreme will, the supreme power, the supreme independent one, and we, being part and parcel of Him, have all these qualities in minute quantity. We have willing, thinking, feeling, and desiring. In the Vedas it is stated that God is the supreme living force among all living forces (cetanaś cetanānām). He is also supplying the necessities of all living entities.

[Book: Science of Self Realization]