Mass Number

20th Jun 2019 @ 13 min read

An atom consists of electrons, protons, and neutrons. Protons and neutrons reside in the nucleus of an atom, and they, in together, are called nucleons. The number of nucleons present in an atom is called mass number. Mass number, as from the name, is responsible for the mass of an atom or atomic mass. Since protons and neutrons are much heavier than electrons, the mass of an atom is estimated by the number of protons and the number of neutrons or in other words, mass number. Mass number is always a whole number because the number of protons and neutrons present in an atom is always a whole number.

Definition

Mass number is the number of nucleons (the sum of protons and neutrons) present in an atom. Mass number is also called as atomic number or nucleon number.

Notation and Formula

Mass number is denoted as A. The value of A is calculated by summing the number of protons and neutron in the nucleus of an atom.

$A =n_\text{p}^{+}+n_\text{n}^{0}$

where: n_p⁺ is the number of protons and n_n⁰ is the number of neutrons.

Representation

The mass number is represented as the left superscript to the symbol of an element. Consider an example of sodium, which has a mass number of 23. The number is superscripted to the left of the symbol of sodium, which is Na (see the below figure). When using the full name of an element, not its symbol, mass number come after the name of an element with a hyphen in between, for example, sodium-23, carbon-12, iron-56.

Mass Number and Atomic Number

Mass number and atomic number are often confusing for beginners, but they both are different. The below table distinguishes them.

Table 1: Mass Number and Atomic Number.
Mass Number	Atomic Number
Mass number is the number of nucleons (protons and neutrons) present in the nucleus of an atom.	Atomic number is the number of protons present in the nucleus of an atom.
It is denoted as A.	It is denoted as Z.
It can be different for a given element, for example, an oxygen atom can have mass number of 16, 17, or 18.	It is always fixed for a given element, for example, the atomic number of an oxygen atom is 16. This is true for any oxygen atom in the universe.
Two different elements can have the same mass number as in ⁴⁰ ₂₀Ca and ⁴⁰ ₁₈Ar.	Two different elements always have a different atomic number as in ⁴⁰ ₂₀Ca and ⁴⁰ ₁₈Ar.
It is always a whole number.	It is also always a whole number.
It is always larger than atomic number (except in the case of ¹ ₁H where both are equal).	It is smaller than mass number (except in the case of ¹ ₁H where both are equal). In fact, atomic number is a subset of mass number.

Mass Number, Atomic Number and Neutron Number

Mass number (A), atomic number (Z), and neutron number (N) relate to each other as simple mathematically equation, which is mentioned below.

Mass Number and Atomic Mass

Mass number is nearly equal to atomic mass of an element. Mass number is a whole number while atomic number occurs in decimals except in the case of carbon-12, which has the exact atomic mass of 12 u. Mass number is a dimensionless quantity while atomic mass is expressed in the atomic mass unit (amu or u). For most of common elements, the difference is very small in the range of (1 u). The difference between them is called mass excess. The table below list some of elements with their mass number and atomic number.

Table 2: Atomic Mass and Mass Number of Various Elements
Element	Atomic Mass, m_a in (u)	Mass Number, A	^m_a∕_A
¹ ₁H	1.007	1	1.007
¹² ₁₂C	12	12	1
²³ ₁₁Na	22.990	23	0.999 56
³⁵ ₁₇Cl	34.969	35	0.999 11
⁵⁶ ₂₆Fe	55.935	56	0.998 84
²⁰² ₈₀Hg	201.971	202	0.999 856
²³⁵ ₉₂U	235.044	235	1.000 187
Note: The atomic mass mentioned in the below table is of isotopic elements; it should not be confused with average atomic mass.

As we can observe from the above table, the ratio of atomic mass to mass number is close to one except in the case of carbon, where it exactly equals one.

Mass Number and Isotopes

Mass number is very useful in distinguishing the isotopes of an element. Isotopes are atoms of the same element which have the same atomic number but a different mass number. Consider an example of uranium, which has two naturally occurring isotopes: uranium-235 (²³⁵
₉₂U) and uranium-238 (²³⁸
₉₂U). Both the isotopes have the same proton number or atomic number. we can differentiate these two by mass number or atomic mass. In fact, we can separate these isotopes with the help of this difference. In uranium enrichment plants, (²³⁵
₉₂U), which is fissile, is separated from (²³⁸
₉₂U) using centrifugation. Centrifugation is a technique in which the constituents are separated using the difference in their masses.

Mass Number in Nuclear Reactions

Nucleons of an atom do not take part in a chemical reaction, only electrons do. Thus, mass number of an element is unaltered in a chemical reaction. But this is not a case with nuclear reactions. In nuclear reactions, mass number may be or may not be altered. Consider the famous uranium fission reaction.

$^{235}_{92}\text{U}\,+\,^1_0\text{n}\, \longrightarrow \,^{139}_{56}\text{Ba}\,+\,^{94}_{36}\text{Kr}\,+\,3{}^{1}_{0}\text{n}$

As we can see, uranium accepts a neutron to form barium and krypton. The mass number of the reactant and the products are different. But in overall reaction the mass number is conserved.

Consider one more example of the natural decay of carbon-14. The carbon-14 is a naturally occurring radioactive isotope, which decays by emitting β-rays. The reaction is as follows:

$^{14}_{6}\text{C}\, \longrightarrow \,^{14}_{7}\text{N}\,+\,\text{e}^-\,+\,\bar{\text{v}}_\text{e}$

In the above reaction, carbon-14 decays to nitrogen-14 by transmitting an electron and an antineutrino. There is a change in atomic number, but mass number is the same in both carbon and nitrogen.

Examples

Example 1: Mass Number of Hydrogen

Statement: Hydrogen atom contain only one proton and no neutron. What is the mass number of the hydrogen atom?

Solution: Since there is only one proton and no neutron, the number of nucleons is one. Thus, mass number is also one.

Example 2: Mass Number of Carbon

Statement: The atomic number of carbon is 6. For an atom of carbon, neutron number also equals 6. What is mass number of the carbon atom?

Solution: The atomic number (Z) is 6 and neutron number (N) is also 6. The mass number (A) is calculated as:

Example 3: Mass Number of Chlorine

Statement: The atomic number of chlorine is 17. For an atom of chlorine, neutron number equals 18. What is mass number of the chlorine atom?

Solution: The atomic number (Z) is 17 and neutron number (N) is 18. The mass number (A) is calculated as:

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