Remember the interpretation of Rutherford's experiment:

If we count the number of impacts of $\alpha$ particles on the photographic paper, we notice that only one particle in $10000$ is deviated by the nucleus.
The gold leaflet had $10000$ gold atoms in thickness.
Let's calculate the diameter of a gold nucleus !

How many particles would be deviated, if the gold leaflet had only a thickness of 1 atom ?

$10000$ times less, therefore one particle in $100 000 000$ !

Imagine the section of a gold atom where the size of the nucleus is exagerated ! What is the ratio of the atom's section area and the nucleus's section area?

$\frac{A_a}{A_n}$ $=$ $100000000$

Imagine the two sections as discs, then calculate !