 # Isotopic Mass

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 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 number; 1, 2 and 3 respectively. Isotopes are found in different percentage in nature. Some of the isotopes are found in abundance whereas some of them are radioactive and decay continually 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.

## Isotopic Mass Definition

On 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 mixture such as the macroscopic mass of oxygen molecule does not correspond to the microscopic mass.

The macroscopic mass implies a certain isotopic distribution while microscopic refers to the mass most common isotope of oxygen that is O-16. Remember the macroscopic mass is also called as 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 the element E can be expressed as:

m(E) = $\sum_{n=1}m(I_{n}) \times p(I_{n})$.

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

= 10.81 Da

## 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 can be defined 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 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 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 of 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 medical and chemical industries.
• Isotopes have the same chemical properties as they have the same number of electrons and their arrangement in the shell.
• They have a different number of neutrons which affects their mass and mass number.
• Their physical properties are different and also depend on their masses.
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