## Volume of an Atom and Nucleus

**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 = r_{0} . A^{1/3}

where r_{0} = 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 4/3πr^{3} or 7,23 ×10^{−45 }m^{3} for hydrogen nuclei or 1721×10^{−45} m^{3} for ^{238}U 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?

**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, r

_{w}, 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**. But this “huge” space is occupied primarily by electrons, because the

^{−30}m^{3}**nucleus**occupies only about

**1721×10**of space. These electrons together weigh only a fraction (let say 0.05%) of entire atom.

^{−45}m^{3}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**“).

We hope, this article, **Volume of an Atom and Nucleus**, helps you. If so, **give us a like** in the sidebar. Main purpose of this website is to help the public to learn some interesting and important information about thermal engineering.