Atomic Number, Mass Number, Isotopes
Structure Of The Atom (Related Concepts)
We have learned about the basic subatomic particles (electrons, protons, neutrons) and the early models of atomic structure. Based on these, we can define and understand some important concepts related to atoms, such as valency, atomic number, mass number, and isotopes.
Valency
The electrons in the outermost shell of an atom are called valence electrons. These electrons are involved in chemical bonding. The number of valence electrons determines the chemical properties of an element.
Valency is defined as the combining capacity of an element. It is the number of electrons that an atom can gain, lose, or share to form chemical bonds with other atoms and achieve a stable electron configuration (usually a complete outermost shell, like that of noble gases, often an octet of 8 electrons or a duet of 2 electrons for elements with only the first shell).
How to determine Valency:
- For elements with up to 4 valence electrons, the valency is usually equal to the number of valence electrons (tendency to lose electrons). Example: Sodium (2, 8, 1) has 1 valence electron, valency = 1. Magnesium (2, 8, 2) has 2 valence electrons, valency = 2. Aluminium (2, 8, 3) has 3 valence electrons, valency = 3.
- For elements with 4 valence electrons, valency is usually 4 (tendency to share electrons). Example: Carbon (2, 4) has 4 valence electrons, valency = 4.
- For elements with more than 4 valence electrons (5, 6, 7), the valency is usually equal to 8 minus the number of valence electrons (tendency to gain electrons to complete the octet). Example: Nitrogen (2, 5) has 5 valence electrons, valency = 8 - 5 = 3. Oxygen (2, 6) has 6 valence electrons, valency = 8 - 6 = 2. Chlorine (2, 8, 7) has 7 valence electrons, valency = 8 - 7 = 1.
- For elements with 8 valence electrons (noble gases, except Helium which has 2), the valency is 0, as they are chemically unreactive and have stable configurations. Example: Neon (2, 8), Argon (2, 8, 8). Helium (2) also has valency 0.
Valency helps us understand and predict how atoms combine to form molecules and write chemical formulae.
Atomic Number And Mass Number
Atoms of different elements are distinguished by the number of protons in their nucleus. The number of protons uniquely identifies an element.
Atomic Number
The atomic number (Z) of an element is equal to the number of protons present in the nucleus of an atom of that element.
Since a neutral atom has an equal number of protons and electrons, the atomic number is also equal to the number of electrons in a neutral atom.
Atomic number is a fundamental property that defines an element. Every element has a unique atomic number.
Example: Hydrogen has 1 proton, so its atomic number (Z) is 1. Carbon has 6 protons, so its atomic number is 6. Oxygen has 8 protons, so its atomic number is 8.
The atomic number is written as a subscript to the left of the element's symbol, e.g., $_1$H, $_6$C, $_8$O.
Mass Number
The mass of an atom is primarily concentrated in its nucleus, which contains protons and neutrons. Electrons have negligible mass compared to protons and neutrons.
The mass number (A) of an atom is the total number of protons and neutrons present in the nucleus of an atom.
$ \text{Mass Number (A)} = \text{Number of protons (Z)} + \text{Number of neutrons (N)} $
So, the number of neutrons in an atom can be calculated as $N = A - Z$.
The mass number is written as a superscript to the left of the element's symbol, e.g., $^1$H, $^{12}$C, $^{16}$O.
A complete representation of an atom showing its atomic number and mass number is $^A_Z X$, where X is the symbol of the element.
Example: Consider an atom represented as $^{23}_{11}\text{Na}$.
- Atomic number (Z) = 11. This means it is Sodium and has 11 protons.
- Since it's a neutral atom, it also has 11 electrons.
- Mass number (A) = 23.
- Number of neutrons (N) = A - Z = 23 - 11 = 12.
Example 1. An atom has 17 protons and 18 neutrons. What is its atomic number, mass number, and name the element?
Answer:
Number of protons = 17.
Atomic number (Z) = Number of protons = 17.
Number of neutrons (N) = 18.
Mass number (A) = Number of protons + Number of neutrons = 17 + 18 = 35.
The element with atomic number 17 is Chlorine (Cl).
Answer: Atomic number = 17, Mass number = 35, Element is Chlorine.
Isotopes
Isotopes are atoms of the same element that have the same atomic number (same number of protons) but different mass numbers (different number of neutrons).
Since isotopes have the same number of protons and electrons (in a neutral atom), they have the same atomic number (Z) and thus exhibit similar chemical properties.
However, since they have different numbers of neutrons, their mass numbers (A) are different, leading to differences in their physical properties (like mass, density, melting point, boiling point) and nuclear stability.
Examples of isotopes:
- Hydrogen: Has three isotopes:
- Protium ($^1_1$H): 1 proton, 0 neutrons, Mass number = 1. This is the most common isotope.
- Deuterium ($^2_1$H or D): 1 proton, 1 neutron, Mass number = 2. Used in heavy water (D$_2$O).
- Tritium ($^3_1$H or T): 1 proton, 2 neutrons, Mass number = 3. This is a radioactive isotope.
- Carbon: Two common isotopes:
- Carbon-12 ($^{12}_6$C): 6 protons, 6 neutrons, Mass number = 12. Used as the standard for atomic mass unit.
- Carbon-14 ($^{14}_6$C): 6 protons, 8 neutrons, Mass number = 14. A radioactive isotope used in radiocarbon dating.
- Chlorine: Has two common isotopes:
- Chlorine-35 ($^{35}_{17}$Cl): 17 protons, 18 neutrons, Mass number = 35.
- Chlorine-37 ($^{37}_{17}$Cl): 17 protons, 20 neutrons, Mass number = 37.
Naturally occurring chlorine is a mixture of these two isotopes in a ratio of approximately 3:1, which is why the average atomic mass of Chlorine is about 35.5 u.
The average atomic mass of an element is the weighted average of the masses of its naturally occurring isotopes. It is calculated based on the abundance of each isotope.
$ \text{Average Atomic Mass} = \sum (\text{Mass of isotope}_i \times \text{Fractional abundance of isotope}_i) $
Example 2. Chlorine exists as two isotopes: $^{35}$Cl (atomic mass 34.9689 u, natural abundance 75.77%) and $^{37}$Cl (atomic mass 36.9659 u, natural abundance 24.23%). Calculate the average atomic mass of Chlorine.
Answer:
Fractional abundance of $^{35}$Cl = 75.77 / 100 = 0.7577
Fractional abundance of $^{37}$Cl = 24.23 / 100 = 0.2423
Average Atomic Mass = (Mass of $^{35}$Cl $\times$ Abundance) + (Mass of $^{37}$Cl $\times$ Abundance)
= $(34.9689 \text{ u} \times 0.7577) + (36.9659 \text{ u} \times 0.2423)$
= $(26.4959 \text{ u}) + (8.9568 \text{ u})$
= $35.4527 \text{ u}$
Answer: The average atomic mass of Chlorine is approximately 35.45 u.
Applications
Isotopes of elements have various applications in different fields:
- Radioactive Isotopes: Isotopes with unstable nuclei that undergo radioactive decay are called radioisotopes.
- Iodine-131 ($^{131}$I): Used in the treatment of goitre (enlarged thyroid gland) and thyroid cancer, and for imaging the thyroid gland.
- Cobalt-60 ($^{60}$Co): Used in cancer therapy (radiotherapy) to kill cancer cells.
- Uranium-235 ($^{235}$U): Used as a fuel in nuclear reactors for generating electricity.
- Carbon-14 ($^{14}$C): Used in radiocarbon dating to determine the age of ancient organic materials (fossils, archaeological artefacts).
- Sodium-24 ($^{24}$Na): Used as a tracer to study blood circulation in the body.
- Stable Isotopes: Isotopes that do not undergo radioactive decay also have applications.
- Deuterium ($^2$H): Used in heavy water (D$_2$O) as a moderator in some nuclear reactors.
- Used as tracers in various chemical and biological studies.
Isobars
Isobars are atoms of different elements that have the same mass number (A) but different atomic numbers (Z).
Since isobars are atoms of different elements, they have different numbers of protons and hence different chemical properties. They also have different numbers of electrons.
However, they have the same total number of protons and neutrons (mass number).
Example: Argon ($^{40}_{18}$Ar) and Calcium ($^{40}_{20}$Ca).
- Argon ($^{40}_{18}$Ar): Atomic number Z=18 (18 protons), Mass number A=40. Number of neutrons = 40 - 18 = 22.
- Calcium ($^{40}_{20}$Ca): Atomic number Z=20 (20 protons), Mass number A=40. Number of neutrons = 40 - 20 = 20.
They are different elements (Argon is a noble gas, Calcium is an alkaline earth metal) with different chemical properties, but they share the same mass number, 40. Other examples include $^{14}_6$C (Carbon) and $^{14}_7$N (Nitrogen).
In summary, isotopes have the same Z but different A (due to different N), while isobars have the same A but different Z (and thus different elements).