Mass Number: Definition, Representation, Isotopes

Mass Number: In the early \(1800\)s, as a part of his research on atoms, John Dalton determined the atomic weights of elements. The early Periodic table developed by Mendeleev was based on Atomic weights of elements. However, after discovering the nucleus, elements in the periodic table were arranged according to increasing atomic numbers. Initially, all atomic weights were measured with respect to hydrogen, which has an atomic weight of one. 

After the discovery of protons, scientists found out that the weight of an atom was mostly due to protons—electrons were known to contribute almost nothing to the atomic weight of the element. It was then found that the atomic weight for an element was often twice the number of protons (or more).  The neutron’s discovery provided the missing part of the picture. Rutherford, in its experiment, proved that the vast majority of the mass of an atom is concentrated in its nucleus, which is composed of protons and neutrons. The atomic mass, now known as the mass number, is the sum of the protons and neutrons in the nucleus.

Mass Number

An atom’s mass number, also called atomic mass number or nucleon number, is the total number of protons and neutrons present in an atomic nucleus. Protons and neutrons are collectively known as nucleons. An electron is almost negligible in weight. Thus, the atomic mass of an atom is almost the same as its mass number.

Representation of Mass Number

The mass number is represented by the letter ‘\({\rm{A}}\).’ The conventional symbol A comes from the German word Atomgewicht which means ‘Atomic weight’.

The mass number of an element is indicated as a left superscript to its elemental symbol. For example, the mass number of Sodium is \(23\), and the atomic number is \(11\). Hence, Sodium can be represented as follows:

Let us consider the element helium; its atomic number is \(2\); hence it has two protons in its nucleus. Its nucleus also contains two neutrons. Hence, \(2 + 2 = 4\), which gives the mass number of the helium atom. As the number of protons must equal the number of electrons, there are two electrons in the helium atom. Similarly, lithium has three protons and four neutrons and a mass number of \(7\).

Fig: Atoms of the First Six Elements

Calculating Mass Number

Knowing the number of neutrons and the atomic number or the number of protons or electrons of an atom, we can determine the mass number of an element.

Mass number = Atomic number + Number of neutrons 

The above formula can be used to determine any one of the three values, provided the other two numbers are known.

For example:

The element chromium \((\text {Cr})\) has an atomic number \(24\) and mass number \(52\). How many neutrons are in the nucleus of a chromium atom? 

To determine the number of neutrons, the atomic number is subtracted from the mass number.

Number of neutrons = mass number − atomic number

\(52 − 24 = 28\)

Hence, there are \(28\) neutrons in a chromium atom, and it is written as \(2452\,\text {Cr}\).

Mass Number and Isotopes

The atomic number of an element represents the number of protons within the atom’s nucleus which is also equal to the number of electrons in the neutral, non-ionized form of the atom. The atomic number gives a unique identity to each element but not to the isotope. This is because an atom of a given element may have a wide range of neutron numbers. The number of protons and neutrons (nucleons) in the nucleus of an atom together contribute to its mass number. However, each isotope of a given element has a different mass number.

Isotopes are two or more types of atoms of the same element that have the same atomic number (number of protons) and position in the periodic table but differ in their nucleon (protons +neutrons) numbers. This happens due to the difference in their mass numbers, resulting in different numbers of neutrons in their nuclei. As the isotopes of a given element have the same atomic number, they exhibit almost the same chemical properties. However, they differ in their physical properties due to different atomic masses. 

For example, \(\text {C}-12, \text {C}-13\), and \(\text {C}-14\) are three isotopes of the element carbon with mass numbers \(12, 13\), and \(14\), respectively. The atomic number of all three isotopes is \(6\), as carbon has an atomic number of \(6\). Hence, in \(\text {C}-12, \text {C}-13\), and \(\text {C}-14\), every carbon atom has \(6\) protons but \(6, 7\), and \(8\) neutrons in their nuclei, respectively.

Mass Number and Radioactive Decay

In the alpha decay of an atom, the nucleus suffers the loss of two neutrons and two protons in the form of an alpha particle. Thus, the atomic number and the number of neutrons each decrease by \(2\). For example, uranium-\(235\) usually disintegrates by alpha decay (Atomic number: \(92 → 90\)), and the mass number decreases by \(4\) (Mass number \(= 235 → 231\)); this results in an atom of thorium \(-231\) and an alpha particle.

On the other hand, in the beta decay of an atom, one neutron is transmuted into a proton with the emission of an electron and an antineutrino. For example, when carbon-\(14\) disintegrates by beta decay, the atomic number increases by \(1\) (Atomic number: \(6\) \(\rightarrow 7\)), and the mass number remains the same (Mass number \(= 14\)); however, the number of neutrons decreases by \(1(\mathrm{~N}: 8 \rightarrow 7)\). The resulting atom is nitrogen\(-14\), with seven protons and seven neutrons.

In gamma-ray emission, all the protons and neutrons remain unchanged in the nucleus; the mass number is also unchanged.

Summary

The number of protons and neutrons (nucleons) in the nucleus of an atom together constitute the atom’s mass number. It is represented by A and is also known as the nucleon number. A chemical element may have the same atomic number but might differ in the nucleon number. This gives rise to isotopes that have the same atomic number but different mass numbers. In this article, we learnt the definition, representation and determination of mass numbers. We also learned how mass number differs in isotopes and the effect on the mass number in radioactive decay.

Frequently Asked Questions (FAQs) on Mass Number

Q.1. How do you find mass numbers from the atomic number and the number of neutrons?
Ans: Mass number = Atomic number + Number of neutrons 

Q.2. Why does Z denote the atomic number?
Ans: The atomic number of an element is conventionally represented by the letter ‘Z’. This is because the letter ‘Z’ comes from the German word Zahl which means ‘number.’ Hence, Atomzahl means atomic number.

Q.3. What is the difference between atomic number and mass number?
Ans: The key difference between atomic number and mass number is that the atomic number represents the number of protons present in an atom which is also equal to the number of electrons surrounding the nucleus of an atom. In contrast, the mass number indicates the total number of nucleons (protons + neutrons) present in an atom.

Q.4. Is the mass number always the same?
Ans: Atoms of the same chemical element do not always have the same mass. This is because the number of protons in the nucleus may be the same for all atoms of the same element, but the number of neutrons may not always be the same. The atoms of an element with the same atomic number but a different mass number are known as isotopes.

Q.5. What is not considered in the mass number?
Ans: An electron does not contribute to the mass number. It is therefore considered nearly massless in comparison with a proton or a neutron. The electron mass is not included in calculating the mass number of an atom.

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