Atomic number and mass number Knowledge-Based Study

Study notes

1. What Defines an Element?

   Every atom consists of a dense central nucleus surrounded by a cloud of electrons. Inside the nucleus are two types of subatomic particles: protons and neutrons.

   The atomic number, represented by the symbol $Z$, is defined as the total number of protons located in the nucleus of an atom:

   $$Z = \text{number of protons}$$

   Key characteristics of the atomic number include:

   • Identity of an Element: The number of protons uniquely determines the chemical identity of an atom. For example, every atom with 6 protons is carbon ($Z = 6$), and every atom with 8 protons is oxygen ($Z = 8$). If the number of protons changes, the atom becomes a completely different element.
   • Neutral Atoms: In an uncharged (neutral) atom, the positive charge of the protons is balanced by an equal number of negatively charged electrons. Therefore, in any neutral atom:

   $$\text{number of electrons} = \text{number of protons} = Z$$

   Understanding Nuclear Mass

   Electrons have an extremely small mass (approximately $1/1836$ the mass of a proton), meaning virtually all of an atom's mass is concentrated within its nucleus. The particles residing in the nucleus—protons and neutrons—are collectively referred to as nucleons.

   The mass number, represented by the symbol $A$, is defined as the total count of nucleons (protons plus neutrons) in an atomic nucleus:

   $$A = \text{number of protons} + \text{number of neutrons}$$

   Since $Z$ represents the number of protons, this relationship can be written as:

   $$A = Z + N$$

   where $N$ represents the number of neutrons.

   Important Note: The mass number $A$ is always an integer count of particles. It should not be confused with the atomic mass or relative atomic mass listed on the periodic table, which is a weighted average of isotopic masses and typically has decimal places.

   Standard Nuclear Notation

   Chemists use standard nuclide notation to summarize the composition of an atom's nucleus. In this notation, the chemical symbol of the element ($\text{X}$) is written with the mass number as a superscript and the atomic number as a subscript to the left:

   $$^{A}_{Z}\text{X}$$

   • $A$ (top left): Mass number (protons + neutrons)
   • $Z$ (bottom left): Atomic number (protons)
   • $\text{X}$: Chemical symbol of the element

   Determining the Number of Neutrons

   By rearranging the mass number equation, the number of neutrons ($N$) in any specific atom or nuclide is readily calculated:

   $$N = A - Z$$

   Subtracting the atomic number from the mass number yields the exact number of neutrons present in that nucleus.

   Step-by-Step Practice

   Example 1: Sodium-23

   Consider the sodium nuclide written as $^{23}_{11}\text{Na}$:

   • Atomic number ($Z$) = 11, so it has 11 protons.
   • In a neutral sodium atom, it also has 11 electrons.
   • Mass number ($A$) = 23.
   • Number of neutrons ($N$) = $A - Z = 23 - 11 =$ 12 neutrons.

   Example 2: Determining Notation from Subatomic Counts

   An atom contains 17 protons, 18 neutrons, and 17 electrons. What are its atomic number, mass number, and standard notation?

   • Atomic number ($Z$) = 17 (element chlorine, $\text{Cl}$).
   • Mass number ($A$) = $17 + 18 = 35$.
   • Standard notation = $^{35}_{17}\text{Cl}$.

   Quick Summary

   • $Z$ (Atomic Number): Number of protons; defines the element.
   • $A$ (Mass Number): Protons + Neutrons; always a whole number.
   • Neutron count: $N = A - Z$.
   • In a neutral atom: $\text{protons} = \text{electrons} = Z$.