# Volume of an Atom and Nucleus

The atom consists of a small but massive nucleus surrounded by a cloud of rapidly moving electrons. The nucleus is composed of protons and neutrons. Typical nuclear radii are of the order 10−14 m. Nuclear radii can be calculated according to the following formula assuming spherical shape:

r = r0 . A1/3

where r0 = 1.2 x 10-15 m = 1.2 fm

If we use this approximation, we, therefore, expect the volume of the nucleus to be of the order of 4/3πr3 or 7,23 ×10−45 m3 for hydrogen nuclei or 1721×10−45 m3 for 238U nuclei. These are volumes of nuclei, and atomic nuclei (protons and neutrons) contain about 99.95% of the atom’s mass.

## Is an atom an empty space?

The volume of an atom is about 15 orders of magnitude larger than the volume of a nucleus. For uranium atom, the Van der Waals radius is about 186 pm = 1.86 ×10−10 m. The Van der Waals radius, rw, of an atom is the radius of an imaginary hard-sphere representing the distance of closest approach for another atom.  The uranium atom has a volume of about  26.9 ×10−30 m3, assuming a spherical shape. But this “huge” space is occupied primarily by electrons because the nucleus occupies only about 1721×10−45 m3 of space. These electrons together weigh only a fraction (let say 0.05%) of the entire atom.

It may seem that the space and, in fact, the matter is empty, but it is not. Due to the quantum nature of electrons, the electrons are not pointing particles, and they are smeared out over the whole atom. The classical description cannot be used to describe things on the atomic scale. On the atomic scale, physicists have found that quantum mechanics describes things very well on that scale. Particle locations in quantum mechanics are not at an exact position, and they are described by a probability density function. Therefore the space in an atom (between electrons and an atomic nucleus) is not empty. Still, it is filled by a probability density function of electrons (usually known as  “electron cloud“).

References:
Reactor Physics and Thermal Hydraulics:
1. J. R. Lamarsh, Introduction to Nuclear Reactor Theory, 2nd ed., Addison-Wesley, Reading, MA (1983).
2. J. R. Lamarsh, A. J. Baratta, Introduction to Nuclear Engineering, 3d ed., Prentice-Hall, 2001, ISBN: 0-201-82498-1.
3. W. M. Stacey, Nuclear Reactor Physics, John Wiley & Sons, 2001, ISBN: 0- 471-39127-1.
4. Glasstone, Sesonske. Nuclear Reactor Engineering: Reactor Systems Engineering, Springer; 4th edition, 1994, ISBN: 978-0412985317
5. Todreas Neil E., Kazimi Mujid S. Nuclear Systems Volume I: Thermal Hydraulic Fundamentals, Second Edition. CRC Press; 2 edition, 2012, ISBN: 978-0415802871
6. Zohuri B., McDaniel P. Thermodynamics in Nuclear Power Plant Systems. Springer; 2015, ISBN: 978-3-319-13419-2
7. Moran Michal J., Shapiro Howard N. Fundamentals of Engineering Thermodynamics, Fifth Edition, John Wiley & Sons, 2006, ISBN: 978-0-470-03037-0
8. Kleinstreuer C. Modern Fluid Dynamics. Springer, 2010, ISBN 978-1-4020-8670-0.
9. U.S. Department of Energy, THERMODYNAMICS, HEAT TRANSFER, AND FLUID FLOW. DOE Fundamentals Handbook, Volume 1, 2, and 3. June 1992.

## See above:

Nuclear Structure