# Atom Calculator

Created by Davide Borchia
Last updated: Sep 14, 2022

Atoms are beautifully arranged on the periodic table: with our atom calculator, we will peek into them, learning how to find the atomic number, calculate the number of protons, neutrons, and electrons, and how to calculate the mass of an atom. Some examples will help you understand how to use the atom calculator and its many functionalities.

## What is an atom? What can we calculate in an atom?

Atoms are the building blocks of nature, the smallest component of matter that still shows the properties we see at our human scale. Atoms showing identical properties belong to the same species: in chemistry, we call each species an element. Hydrogen is an element; tellurium, oxygen, and uranium are all elements.

Atoms are a collection of three particles: protons, neutrons, and electrons. The different proportions of such components define uniquely an atom.

Atoms are neatly arranged in the periodic table: the table divides elements

Currently, we model atoms using the orbital model, an improvement over the Bohr model (if you are curious, visit our Bohr model calculator).

## How to calculate protons, neutrons, and electrons: how to find the atomic number and much more

The most crucial quantity we use to define an atom is the atomic number $Z$. The atomic number is a nuclear quantity describing the number of protons in the nucleus How to find the atomic number? The periodic table comes in our help: counting as if you were reading (from left to right, from top to bottom), the position of an element corresponds to their atomic number.

For example, oxygen has atomic number $Z=8$, while tungsten has atomic number $Z=74$.

Remaining in the nucleus, we find neutrons. The number of neutrons is not constant for a given element: there is usually a number that appears more frequently that we can take as a reference, but we can find lighter and heavier elements.

The number of neutrons is not given as a specific number when we write an atomic symbol: we count them together with protons in the mass number $A$

Examples of isotopes are, for hydrogen, deuterium and tritium, respectively, with one and two neutrons. Carbon has a famous isotope with mass number $A=14$ widely used in dating samples thousands of years old.

Together, atomic number and mass number allow us to write the element in an identifiable way using the AZE notation. The acronym will be clear in a second:

• $A$ is the mass number;
• $Z$ is the calculated atomic number; and
• $E$ is the chemical symbol of the element.
$^{{A}}_{Z}\text E$

For hydrogen, we have:

• $A = 1$;
• $Z = 1$; and
• $E = \text H$.

Its notation is:

$^1_1\text H$

For the fissile isotope of uranium, we have:

• $A = 235$;
• $Z = 92$; and
• $E = \text U$.
$^{235}_{92}\text U$

#### How to find the charge of an atom: how to calculate the number of electrons

The nucleus is done. We can pay attention to the electrons. Electrons are smaller than protons and neutrons, and their number doesn't affect the mass of an atom in any excessive way. However, their charge is all but negligible: we use it to measure all other charges (we call it the fundamental charge). Protons have an identical charge but opposite sign: by convention, electrons are negative and protons positive.

Atoms try to reach neutrality; in their stable and most common state, they are electrically neutral: this means that the number of electrons and protons is the same.

You can use the charge of an atom to calculate the number of electrons: a positive charge indicates an imbalance toward protons, a negative one toward electrons, following the relationship:

$c = Z - n_{\text{e}}$

In the formula about how to find the charge of an atom, we can find:

• $c$ — The charge; and
• $n_{\text{e}}$ — The number of electrons.

## How to calculate the mass of an atom

After learning how to calculate protons, neutrons, and electrons, we can learn how to find the charge of an atom. The formula is straightforward:

$m \!=\! Z\!\cdot\! m_{\text{p}} + (A\!-\!Z)\!\cdot\! m_{\text{n}} + n_{\text{e}}\!\cdot \!m_{\text{e}}$

Where:

• $m_{\text{}}=1.67262192 \times10^{-27}\ \text{kg}$ — The mass of the proton;
• $m_{\text{}}=1.67492749\times10^{-27}\ \text{kg}$ — The mass of the neutron; and
• $m_{\text{}}=9.1093837\times10^{-31}\ \text{kg}$ — The mass of the electron.

The kilogram is not a suitable unit for these measurements: the preferred one is the atomic mass unit, a twelfth of the mass of a carbon-12 atom. With this new measurement unit, the masses of the subatomic particles composing the atoms are:

• $m_{\text{}}=1.00727646\ \text{u}$ — The mass of the proton;
• $m_{\text{}}=1.00866491\ \text{u}$ — The mass of the neutron; and
• $m_{\text{}}=5.485799\times10^{-4}\ \text{u}$ — The mass of the electron.

The atomic mass unit is widely employed in chemistry: learn other uses with our molecular weight calculator and peptide molecular weight calculator.

Neutrons are slightly heavier than protons. This imperceptible imbalance ($0.1\%$) allows the universe to exist as we know it: neutrons decay in protons and electrons — the process is the known beta decay —, not the other way around. Only neutrons accompanied by protons are stabilized enough to avoid that fate. If proton had been the heavier ones, hydrogen, with its sole proton, would have had a hard time being around!

Let's calculate an atom's mass: take the stable isotope of tellurium, $^{120}_{52}\text{Te}$.

🙋 Remember that the atom is neutral: its charge is $c=0$, hence $n_{\text{e}}=Z$.

\begin{align*} m_{\text{Te}} &= 52\cdot 1.00727646 \\ &+ (120-52)\cdot 1.00866491 \\ &+ 52\cdot 5.485799\times10^{-4}\\ &=120.9961\ \text{u} \end{align*}

🙋 For other tools about the fundamental elements of nature, visit our photoelectric effect calculator and our quantum number calculator!

Davide Borchia
Atomic number
Mass number
Charge
Atomic composition
Number of protons
Number of neutrons
Number of electrons
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