An atom is composed of electrons, protons and neutrons. The total number of protons in an atom is called the atomic number. The sum of the number of neutrons and protons is known as the mass number. In an atom, the number of protons is always equal to the total number of electrons which makes it neutral due to equal and opposite charges of electrons and protons.
The atomic mass is expressed in unified atomic mass units (u). Some of the atoms contain the same number of protons but a different mass number due to a different number of neutrons. They are called isotopes. For example; three isotopes of hydrogen are; hydrogen (H), deuterium (D) and tritium (T).
They have the same atomic number but different mass numbers; 1, 2 and 3 respectively. Isotopes are found in different percentages in nature. Some of the isotopes are found in abundance whereas some of them are radioactive and decay continuously in nature. For example; C-12 is the most abundant isotope of carbon whereas C-14 is a radioactive isotope of it with a half-life of 5500 years.
Table of Contents
- Isotopic Mass Definition
- How to Find Isotopic Mass?
- Relative Isotopic Masses
- Average Isotopic Mass
- Table of Isotopic Masses
- Uses of isotopes
- Frequently Asked Questions
Isotopic Mass Definition
Isotopic mass refers to the average mass of all the isotopes of a specific element. At a macroscopic level, most mass measurements of pure substances give the mass of a mixture of isotopes. In other words, we can say that mixtures are not pure but the mixture of all known mixtures such as the macroscopic mass of an oxygen molecule does not correspond to the microscopic mass.
The macroscopic mass implies a certain isotopic distribution while microscopic refers to the mass of the most common isotope of oxygen that is O-16. Remember the macroscopic mass is also called molecular weight or atomic weight.
How to Find Isotopic Mass?
We know that isotopes are atoms with the same atomic number but different mass numbers due to a different number of neutrons. The mass number of an element is a whole number whereas the actual mass of an atom is not a whole number except for carbon-12.
For example, the atomic mass of Lithium is 6.941 Da. On the basis of the abundance of isotopes, we can calculate the isotopic mass and average atomic mass of an element. The average mass of element E can be expressed as:
For example, the mass and abundance of isotopes of Boron are given below.
| 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 Boron can be calculated as:
m(B) = (10.013)(0.199)+(11.009)(0.801)
=1.99 +8.82
Relative Isotopic Masses
It’s difficult to express the mass of an element, relative mass is one of the best methods to express the mass of known elements. It is represented as ‘Ar’;
Ar = m/mu
The relative isotopic mass is a unitless quantity with respect to some standard mass quantity. The relative atomic mass can be taken as the weighted mean mass of an atom of an element compared to the mass of 1/12 of the mass of an atom in C-12.
Similarly relative isotopic mass is referred to as the mass of an atom of an isotope with respect to the mass of 1/12 of the mass of an atom in C-12. The isotopic abundances are used to calculate the average atomic weight and isotopic weights.
Average Isotopic Mass
The percentage of abundance and isotopic mass is used to calculate the average isotopic mass. For example, two isotopes of Nitrogen are N-14 and N-15 and the average isotopic mass of Nitrogen is 14.007. The percentage abundance of both isotopes can be calculated as given below.
(14.003074) (x) + (15.000108) (1 – x) = 14.007
(14) (x) + (15) (1 – x) = 14.007
x = 15 – 14.007 = 0.993
1 – x = 0.007
So the percentage abundance of N-14 would be 99.3 % and for N-15 it would be 0.7 %. Similarly, we have the average isotopic mass of copper is 63.546 and the atomic mass of Cu-63 is 62.929 amu and Cu-65 is 64.927 amu, the percentage abundance would be;
(62.9296) (x) + (64.9278) (1 – x) = 63.546
x = 0.6915
Hence the percentage abundance of Cu-63 would be 69.15 % and the rest would be Cu-65.
Table of Isotopic Masses
| Isotopic | Isotopic Mass |
| Cl – 35 | 34.969 amu |
| Cl – 37 | 36.966 amu |
| Si – 28 | 27.9769 amu |
| Si – 29 | 28.9765 amu |
| Si – 30 | 29.9738 amu |
| Fe – 54 | 53.9396 amu |
| Fe – 56 | 55.9349 amu |
| Fe – 57 | 56.9354 amu |
| Fe – -58 | 57.9333 amu |
| Sr – 84 | 83.9134 amu |
| Sr – 86 | 85.9094 amu |
| Sr -87 | 86.9089 amu |
| Sr – 88 | 87.9056 amu |
| O – 15 | 15.995 amu |
| O – 16 | 16.999 amu |
| O – 17 | 17.999 amu |
| Pb – 206 | 205.98 amu |
| Pb – 207 | 206.98 amu |
| Pb -208 | 20.98 amu |
| Ne – 20 | 1.99 amu |
| Ne – 22 | 21.99 amu |
| Ne -21 | 20.9938 amu |
| Rb -85 | 84.9117 amu |
| Rb – 87 | 86.9086 amu |
Uses of isotopes
- Some of the isotopes are very useful and widely used in various fields like the medical and chemical industries.
- In the medical field, isotopes are used by doctors to diagnose and treat diseases such as heart disease and cancer.
