# Isotopic Mass

## Introduction

An atom can be composed of electrons, protons, neutrons. The total number of protons present in an atom is referred to as the atomic number. Moreover, the sum of the number of neutrons and protons is called the mass number. In any atom, the number of protons is continually equal to the total number of electrons, making it neutral because of the equal and opposite charges of both electrons and protons.

### Expressing Atomic Mass

The atomic mass can be expressed using unified atomic mass units (u). A few of the atoms hold the same number of protons but with a different mass number because of many neutrons, and these are called isotopes. For instance; 3 hydrogen'>isotopes of hydrogen can be given as deuterium (D), hydrogen (H), tritium (T).

They contain the same atomic number, whereas the mass numbers are different, which are 1, 2, 3, respectively. Isotopes can be found in different percentages in nature. A few of the isotopes can be found in abundance, but a few of them decay and undergo radioactivity continually in nature. For suppose; C-12 is given as the most abundant isotope of carbon, and, on the other side, C-14 is a radioactive isotope of it, each with a half-life of 5500 years.

### Isotopic Mass Definition

At the macroscopic level, most of the mass measurements of pure substances give the mass of an isotope mixture. We can also say, in other words, that mixtures are not pure, but of all known mixture like the oxygen molecule's macroscopic mass does not correspond to the microscopic mass.

The macroscopic mass indicates a certain isotopic distribution, whereas the microscopic mass refers to the mass of the most common isotope of oxygen, O-16. It should be remembered that the macroscopic mass can also be called either atomic weight or molecular weight.

### How to Find Isotopic Mass?

As we all know, isotopes are atoms that have the same atomic number but with different numbers because of the different neutron numbers. The mass number of an element is given as a whole number, whereas the atom's actual mass is not a whole number except for the carbon-12.

For suppose, the atomic mass of Lithium is given as 6.941 Da. Based on the abundance of isotopes, we can calculate the average atomic mass and isotopic mass of an element. The average mass of the element E is expressed as:

m(E)=n=1m(In) p(In)

For example, the abundance and mass of isotopes of Boron can be given as follows.

 S. No Isotope In Mass m (Da) Isotopic Abundance p 1 10B 10.013 0.199 2 11B 11.009 0.801

The average mass of the Boron is calculated as follows.

m(B) = (10.013 0.199) + (11.009 0.801)

=(1.99) + (8.82)

= 10.81 Da

### Relative Isotopic Masses

It is not easy to express an element's mass since relative isotopic masses are one of the best methods to express the known elements' mass. We can define it as 'Ar';

Ar = m/mu

The relative isotopic mass is given as a unitless quantity concerning some standard mass quantity. The relative atomic mass of elements is taken as the atom's weighted mean mass of an element to that of the mass of 1/12 of the mass of an atom in the C-12 element.

In the same way, the relative isotopic mass is referred to as the atom's mass of an isotope concerning the mass of 1/12 of the mass of an atom in the C-12 element. The isotopic abundances can be used to calculate the isotopic weights and average atomic weight.

### Average Isotopic Mass

The percentage of isotopic mass and abundance can be used to calculate the average isotopic mass. For instance, two isotopes of Nitrogen are given as N-14, N-15, and Nitrogen's average isotopic mass can be given as 14.007. The percentage abundance of both the isotopes is calculated as follows.

14.003074 x Х + 15.000108 x 1 - Х = 14.007

14 x Х+ 15 x 1 - Х = 14.007

X = 15 - 14.007 = 0.993

1 - X = 0.007

Thus, 99.3 % would be the percentage abundance of N-14, whereas, for N-15, it would be 0.7%. In the same way, the copper's average isotopic mass is given by 63.546, and the atomic mass of Cu-63 is given as 62.929 amu, and the Cu-65, as 64.927 amu, where the resultant abundance percentage would be given as follows.

62.9296 x Х + 64.9278 x 1 - Х = 63.546

Therefore, x = 0.6915

Thus, 69.15 % would be the percentage abundance of Cu-63, whereas the rest would be Cu-65.

### Uses of Isotopes

A few of the uses of Isotopes can be given as follows.

• A few of the isotopes are very useful and can be used widely in various chemical and medical industries.

• Isotopes also contain similar chemical properties because they contain the same electron number and their shell arrangement.

• The physical properties of isotopes vary and they also depend on their masses.

Q1. Give Some Uses of Isotopes?

Ans. A few of the uses of Isotopes can be given as follows.

• The physical properties of isotopes are different and also depend on their masses.

• They contain a different number of neutrons, which affects both their mass number and mass.

Q2. Why the Isotopes' Atomic Mass Not a Whole Number?

Ans. The atomic mass of an atom is given as the sum of the quantities of protons and neutrons present in the nucleus, which is a whole number. On the other side, atoms of a specific element do not all have similar neutron numbers, so a macroscopic sample of the element will have atoms of different weights. The resulting fraction can be given as the weighted average atomic mass, which takes place naturally.

Q3. Why Isotopes Holds Different Mass Numbers?

Ans. Since different isotopes contain different neutron numbers, they all do not weigh the same or hold the same mass. Different isotopes of the similar element contain a similar atomic number. They contain the same number of protons. The proton number can decide the atomic number.

Q4. Why Isotopes Contain Different Melting Points?

Ans. The atomic mass of most elements is fractional and they occur as a combination of isotopes of varying masses. Furthermore, most elements occur in nature as a isotopes' mixture of different masses. Fractional atomic masses arise due to this mixture only.

Average mass = Total mass of overall atoms/number of atoms.