Volume of an Atom and Nucleus

Volume of an Atom and Nucleus

Structure of Matter.
Structure of Matter.

The atom consist 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. Assuming spherical shape, nuclear radii can be calculated according to following formula:

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) contains of about 99.95% of mass of atom.

Is an atom an empty space?

atomic-nucleus-volume-min
A figurative depiction of the helium-4 atom with the electron cloud in shades of gray. Protons and neutrons are most likely found in exactly the same space, at the central point. Source wikipedia.org License CC BY-SA 3.0

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.  Assuming spherical shape, the uranium atom have volume of about  26.9 ×10−30 m3. 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 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 point particles, 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, they are described by a probability density function. Therefore the space in an atom (between electrons and an atomic nucleus) is not empty, but it is filled by a probability density function of electrons (usually known as  “electron cloud“).

See above:

Nuclear Structure