Matter, well, matters. Atoms, either singly as elements or in groups of molecules, make up all matter. The actions, interactions and reactions of atoms cause and create the physical world. The world therefore depends on the balance, and imbalance, of protons, neutrons and electrons in atoms, isotopes and ions.
TL;DR (Too Long; Didn't Read)
The number of protons in atoms, isotopes and ions equals the atomic number of the element. The number of neutrons equals the mass number of the atom minus the atomic number. The atomic number and average atomic mass (the weighted average of the mass number of all isotopes) can be found on the Periodic Table. The number of electrons in neutral atoms and isotopes equals the number of protons. In ions, the number of electrons equals the number of protons plus or minus the opposite of the charge on the ion. An ion with a plus two (+2) charge has two less electrons than protons. An ion with a minus one (-1) charge has one more electron than protons.
All atoms consist of many tiny particles, with the three main particles being protons, neutrons and electrons. The nucleus, the center of the atom, contains the atom's protons and neutrons. Electrons circle around the nucleus. Protons carry positive charges. Neutrons do not have any charge. Electrons have negative charges. In a neutral atom, an atom without any positive or negative charge, the number of protons equals the number of electrons. The number of neutrons in the nucleus may vary, however.
Ordering the Atoms
The Periodic Table of Elements places the elements in order by atomic number. Building on the work of many scientists, Dmitri Mendeleev organized the Periodic Table based on atomic mass. With increased understanding of atomic structure, a slight organizational change to the Periodic Table resulted in the order seen today, with elements in order by the number of protons. So, hydrogen, number one on the Periodic Table, contains one proton in its nucleus. Helium, number two on the Periodic Table, has two protons in its nucleus. Platinum, number 78, has 78 protons.
Atoms, Isotopes and Ions
All the atoms of an element contain the same number of protons. All atoms of carbon have 6 protons. All atoms of lead have 82 protons. But, not all atoms of an element have the same mass. Carbon atoms usually have a mass number of 12 but may have a mass number of 13 or 14. Lead usually has a mass number of 208 but may have a mass number of 207, 206 or 204. Atoms with the same atomic number but different mass numbers are called isotopes. So, really, atoms and isotopes are synonymous terms. Different isotopes of an element remain variations of the same atom.
The shorthand notation for isotopes shows the element name or symbol followed by the isotope mass number. For example, carbon with a mass number of 12 would be written carbon-12 or C-12. Lead with a mass number 208 would be written lead-208 or Pb-208. Alternately, the isotope may be written like this: 20882Pb.
Ions occur when an atom gains or loses electrons. Elements gain or lose electrons with varying degrees of ease. Some atoms gain electrons easily while others lose electrons easily. With a few exceptions, atoms either gain or lose electrons, but they don't do both. Carbon, one of the exceptions, can gain or lose its four valence (outer layer, or shell) electrons. Chemistry shorthand for ions shows the chemical symbol with the charge imbalance written as a superscript. For example, a lithium ion would be written as Li+1.
Finding the number of protons requires reading the Periodic Table rather than doing any calculations. Whether an atom, an isotope or an ion, the atomic number equals the number of protons. If the atomic number is 18 (argon), the number of protons equals 18. Atomic number 3 (lithium) means the element has 3 protons. Find the atomic number of the element on the Periodic Table to find the number of protons.
The mass number of an atom equals the number of protons plus the number of neutrons. Rearranging the equation, the number of neutrons equals the mass number minus the atomic number. Remember, the atomic number equals the number of protons. So, the mass number of lead, 208, minus the atomic number, 82, equals 126. Mathematically speaking, 208-82=126, or 126 neutrons in the most common lead isotope. The isotope lead-204 has 122 neutrons because 204-82=122. A quick caveat: The atomic mass shown on the Periodic Table generally shows the weighted average mass of all the isotopes of the element.
In atoms and isotopes, calculating the number of electrons requires remembering that in a neutral atom or a neutral isotope the positive and negative charges will be equal. In other words, the number of electrons equals the number of protons. Finding the atomic number on the Periodic Table gives not only the number of protons but also the number of electrons in a neutral atom or isotope.
In an unbalanced atom or isotope, the number of protons doesn't equal the number of electrons. The difference between the two particles results from an imbalance of positive and negative charges. So, an atom with an ionic charge of +2 has two more protons than electrons. The element calcium, for example, has atomic number 20 so the atom has 20 protons. The calcium ion with a positive +2 charge has two more protons than electrons. Calculating the number of electrons becomes 20-2=18, or 18 electrons. On the other side of the Periodic Table, fluorine, atomic number 9, has 9 protons and often forms an ion with a -1 charge by adding an extra electron to its outer shell. In this case, the atom has one more negative electron than positive protons. Mathematically, calculate the total number of electrons by adding one electron to the number of protons, 9+1=10. Therefore, the fluorine ion has 9 protons and 10 electrons.