Question

What is the size of the nucleus of an atom compared to its atomic radius?

Answer 1

On an order of magnitude, an atom has a diameter of
\[ d_{atom} = 10^{-10} \ m \]
and the nucleus
\[ d_{nucleus} = 10^{-14} \ m \]

The ratio of the two is
\[ \frac{d_{atom}}{ d_{nucleus}} = \frac{10^{-10}}{10^{-14}} = 10^4 = 10,000 \]
Hence a nucleus is 10,000 wider than the nucleus.

In terms of volume, this means the atom has
\[ (10,000)^3 = 1,000,000,000 \]
times more volume than a nucleus.

You might also enjoy the first five minutes of this lecture:
http://ocw.mit.edu/courses/physics/8-02-electricity-and-magnetism-spring-2002/video-lectures/lecture-1-what-holds-our-world-together/

Answer 2

**correction
\[ (10,000)^3 = 1,000,000,000,000 \]
!!