Atomic Number, Mass Number & Nuclide Notation - Ninth Grade Science
What defines the chemical identity of an element? What makes a shiny nugget of gold behave fundamentally differently from a bar of silver or a cylinder of compressed oxygen gas? The answer resides within the atomic nucleus. The number of positively charged protons packed into that central core serves as an element's unique chemical fingerprint. In 1913, English physicist Henry Moseley established that the physical and chemical properties of elements are periodic functions of their atomic numbers, not their atomic masses. Alongside the atomic number, an atom is characterized by its mass number, the total tally of nucleons in its nucleus. In this chapter, you will master the definitions of atomic number ($Z$) and mass number ($A$), learn standard IUPAC nuclide notation, and calculate protons, neutrons, and electrons in neutral atoms and ions.
The Atomic Number ($Z$): The Elemental Fingerprint
The atomic number of an element, universally represented by the symbol $Z$ (from the German word *Zahl*, meaning number), is defined as the total number of protons present in the nucleus of an atom of that element.
+--------------------------------------------------------------------------+
| Atomic Number (Z) |
+--------------------------------------------------------------------------+
| Definition: Total number of protons in the atomic nucleus |
| Formula: Z = Number of Protons (p+) |
| In Neutral: Z = Number of Protons = Number of Electrons (e-) |
| Rule: Unique to each element; NEVER changes in chemical reactions |
+--------------------------------------------------------------------------+
Atomic Number Identifies the Element
Z = 1 ===> 1 Proton ===> Hydrogen (H)
Z = 6 ===> 6 Protons ===> Carbon (C)
Z = 7 ===> 7 Protons ===> Nitrogen (N)
Z = 8 ===> 8 Protons ===> Oxygen (O)
Z = 79 ===> 79 Protons ===> Gold (Au)
The Invariance of Atomic Number
The atomic number defines the element: every atom in the universe that contains exactly six protons is a carbon atom, and every atom containing seventy-nine protons is a gold atom. If you add or remove a proton from a nucleus, you transmute the element into an entirely different chemical substance. In any neutral atom, the number of negatively charged orbital electrons equals the atomic number ($Z = ext{protons} = ext{electrons}$), ensuring electrical neutrality.
The Mass Number ($A$): Tallying Nucleons
The mass number of an atom, denoted by the symbol $A$, is defined as the total sum of the number of protons and neutrons present in the nucleus of that atom.
+--------------------------------------------------------------------------+
| Mass Number (A) |
+--------------------------------------------------------------------------+
| Definition: Total number of nucleons (protons + neutrons) in nucleus |
| Formula: A = Number of Protons (Z) + Number of Neutrons (n) |
| A = Z + n |
| Rearranged: Number of Neutrons n = A - Z |
+--------------------------------------------------------------------------+
The Composition of the Mass Number
MASS NUMBER (A)
|
+--------------+--------------+
| |
Protons (Z) Neutrons (n)
[ Positive ] [ Neutral ]
Nucleons = Protons + Neutrons
Why Electrons are Omitted from the Mass Number
Recall that an electron possesses an mass of only $\frac{1}{1836} ext{ u}$, contributing less than 0.05% of an atom's mass. In contrast, protons and neutrons each have a mass of approximately one atomic mass unit ($1 ext{ u}$). Therefore, the mass number $A$ is an integer that represents the approximate mass of the atom in unified atomic mass units ($u$). The protons and neutrons reside together in the compact central nucleus and are referred to collectively as nucleons.
Calculating Neutrons: $n = A - Z$
To determine the number of neutrons ($n$) in any atomic nucleus, subtract the atomic number ($Z$) from the mass number ($A$):
n = A - Z
For example, a sodium atom with a mass number $A = 23$ and atomic number $Z = 11$ contains:
n = 23 - 11 = 12\text{ neutrons}
Standard IUPAC Nuclide Notation
To convey the complete subatomic composition of an atom or ion in a standardized format, IUPAC established nuclide notation:
Standard IUPAC Nuclide Notation
Mass Number (A) ---> A
X <--- Chemical Symbol
Atomic Number (Z) ---> Z
Examples:
12 23 35
C Na Cl
6 11 17
(Carbon-12) (Sodium-23) (Chlorine-35)
In standard nuclide notation:
- The chemical symbol of the element ($X$) is written centrally.
- The mass number ($A$) is written as a superscript to the left of the symbol.
- The atomic number ($Z$) is written as a subscript to the left of the symbol.
When expressing an atom in text, chemists often use the element name followed by a hyphen and the mass number, such as carbon-12 ($^{12} ext{C}$), uranium-235 ($^{235} ext{U}$), or cobalt-60 ($^{60} ext{Co}$).
Subatomic Calculations in Ions
When neutral atoms participate in chemical reactions, they can gain or lose electrons, forming ions. Protons and neutrons reside within the nucleus and remain unchanged during chemical reactions; only the electron count changes.
+-----------------------+--------------------------------------------------+
| Ionic Species | Electron Calculation Formula |
+-----------------------+--------------------------------------------------+
| Neutral Atom | Number of Electrons = Z |
| Cation (Positive Ion) | Number of Electrons = Z - (Magnitude of Charge) |
| Anion (Negative Ion) | Number of Electrons = Z + (Magnitude of Charge) |
+-----------------------+--------------------------------------------------+
Case 1: Aluminum Cation (Al^3+, Z = 13, A = 27)
Protons = Z = 13
Neutrons = A - Z = 27 - 13 = 14
Electrons= Z - (+3 charge) = 13 - 3 = 10 electrons
Case 2: Oxide Anion (O^2-, Z = 8, A = 16)
Protons = Z = 8
Neutrons = A - Z = 16 - 8 = 8
Electrons= Z - (-2 charge) = 8 + 2 = 10 electrons
Both $ ext{Al}^{3+}$ and $ ext{O}^{2-}$ have ten electrons, achieving stable neon-like configurations ($2, 8$).
Chapter Exercises
Exercise 1: An atom of an element is represented in nuclide notation as $_{19}^{39} ext{K}$. Identify the chemical name of the element, state its atomic number and mass number, and calculate the number of protons, neutrons, and electrons present in a neutral atom of this element.
Exercise 2: Determine the complete subatomic particle composition (number of protons, neutrons, and electrons) for each of the following four chemical species: (a) Neutral iron atom: $*{26}^{56} ext{Fe}$ (b) Sulfide anion: $*{16}^{32} ext{S}^{2-}$ (c) Calcium cation: $*{20}^{40} ext{Ca}^{2+}$ (d) Deuterium atom: $*{1}^{2} ext{H}$
Exercise 3: An ion $ ext{X}^{3+}$ contains 10 electrons and 14 neutrons. Calculate the atomic number of element X, identify the element on the periodic table, determine the mass number of this nuclide, and write its complete symbol in standard IUPAC nuclide notation.
Solutions and Explanations
Solution 1: The symbol $ ext{K}$ represents the element potassium. From the nuclide notation $_{19}^{39} ext{K}$: the subscript is the atomic number $Z = 19$, and the superscript is the mass number $A = 39$. The number of protons equals the atomic number: $ ext{protons} = 19$. In a neutral atom, the number of electrons equals the number of protons: $ ext{electrons} = 19$. The number of neutrons is the mass number minus the atomic number: $ ext{neutrons} = A - Z = 39 - 19 = 20$ neutrons.
Solution 2: Calculating subatomic particles for each species: (a) For neutral iron ($*{26}^{56} ext{Fe}$): Atomic number $Z = 26$, mass number $A = 56$. Protons $= 26$; Neutrons $= 56 - 26 = 30$; Electrons $= 26$ (neutral). (b) For sulfide anion ($*{16}^{32} ext{S}^{2-}$): Atomic number $Z = 16$, mass number $A = 32$. Protons $= 16$; Neutrons $= 32 - 16 = 16$; Electrons $= 16 - (-2) = 16 + 2 = 18$ electrons. (c) For calcium cation ($*{20}^{40} ext{Ca}^{2+}$): Atomic number $Z = 20$, mass number $A = 40$. Protons $= 20$; Neutrons $= 40 - 20 = 20$; Electrons $= 20 - 2 = 18$ electrons. (d) For deuterium ($*{1}^{2} ext{H}$): Atomic number $Z = 1$, mass number $A = 2$. Protons $= 1$; Neutrons $= 2 - 1 = 1$; Electrons $= 1$ (neutral).
Solution 3: The ion carries a $+3$ charge, meaning the neutral atom lost three electrons to form $ ext{X}^{3+}$. The number of electrons in the neutral atom is: $ ext{electrons} = 10 + 3 = 13$. In a neutral atom, the number of protons equals the number of electrons, so atomic number $Z = 13$. The element with atomic number 13 is aluminum ($ ext{Al}$). The mass number is the sum of protons and neutrons: $A = Z + n = 13 + 14 = 27$. The nuclide notation for this ion is: $_{13}^{27} ext{Al}^{3+}$.