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# Calculation of empty space in an atom (considering the simplest hydrogen atom)

Atoms are the basic units of matter and the defining structure of the elements. Atoms are made up of three particles: protons, neutrons, and electrons.

Protons and neutrons are heavier than electrons and reside in the center of the atom, which is called the nucleus. Electrons are extremely light and exist in a cloud that orbits around the nucleus. The electron cloud has a radius 10,000 times larger than the nucleus.

Protons and neutrons have roughly the same mass. However, a proton weighs more than 1,800 electrons. Atoms always have the same number of protons and electrons, and the number of protons and neutrons is usually the same as well. Adding a proton to an atom creates a new element, while adding a neutron creates an isotope, or heavier version, of that atom.

Nucleus

The nucleus was discovered in 1911, but its parts were not identified until 1932. Virtually all of the mass of the atom resides in the nucleus. The core is held together by the “strong force”, one of the four basic forces of nature. This force between the protons and neutrons overcomes the repulsive electrical force that, according to the rules of electricity, would push the protons apart.

protons

Protons are positively charged particles found inside atomic nuclei. They were discovered by Ernest Rutherford in experiments conducted between 1911 and 1919.

The number of protons in an atom defines what element it is. For example, carbon atoms have six protons, hydrogen atoms have one, and oxygen atoms have eight. The number of protons in an atom is known as the atomic number of that element. The number of protons in an atom also determines the chemical behavior of the element. The Periodic Table of the Elements arranges the elements in order of increasing atomic number.

Protons are made of other particles called quarks. There are three quarks in each proton, two “up” quarks and one “down” quark, and they are held together by other particles called gluons.

electrons

Electrons are negatively charged and are electrically attracted to positively charged protons. Electrons surround the atomic nucleus in paths called orbitals. The inner orbitals that surround the atom are spherical, but the outer orbitals are much more complicated.

The electron configuration of an atom is the orbital description of the locations of the electrons in an unexcited atom. Using the electron configuration and the principles of physics, chemists can predict the properties of an atom, such as stability, boiling point, and conductivity.

Usually only the outermost electron shells are important in chemistry. The inner electron shell notation is often truncated by replacing the longhand orbital description with the symbol for a noble gas in parentheses. This method of notation greatly simplifies the description of large molecules.

For example, the electron configuration of beryllium (Be) is 1s22s2, but it is written [He]2s2. [He] it is equivalent to all the electron orbitals in a helium atom. The letters s, p, d and f designate the shape of the orbitals and the superscript indicates the number of electrons in that orbital.

neutrons

Neutrons are uncharged particles found inside atomic nuclei. The mass of a neutron is slightly greater than that of a proton. Like protons, neutrons are also made of quarks: one “up” quark and two “down” quarks. Neutrons were discovered by James Chadwick in 1932.

Most. Let’s take a look at a hydrogen atom to see how empty it really is.

A hydrogen atom is made of a single proton that is surrounded by a single electron. How big is a hydrogen atom? The radius of a hydrogen atom is known as the Bohr Radius, which is equal to .529 × 10-10 meters. That means that a hydrogen atom has a volume of about 6.2 × 10-31 cubic meters.

How big is the proton at the center of a hydrogen atom? Recent studies indicate that protons have a radius of about 0.84 × 10-15 meters, giving them a volume of about 2.5 × 10-45 cubic meters.

We need to do a little more math to figure out how much of a hydrogen atom is empty space:

Fill Percentage = 100 × (Filled Volume/Total Volume)

Full percentage = 100 × (2.5 × 10**-45 m3 / 6.2 × 10**-31 m3)

Percent full = 100 × (4 × 10**-15)

Percent Full = 4 × 10**-13%

Percent full = 0.0000000000004%

If 0.0000000000000000004% of a hydrogen atom is full, then the rest must be empty:

Percent Empty = 100% – Percent Full

Empty percentage = 100% – 0.0000000000004%

Empty percentage = 99.9999999999996%

A hydrogen atom is approximately 99.9999999999996% empty space. Put another way, if a hydrogen atom were the size of Earth, the proton at its center would be about 200 meters (600 feet) wide. While I wouldn’t want something that big to fall on my head, it is small compared to the size of the earth.