Relative Atomic Mass

The relative Atomic mass of an element is the number of times the average mass of one atom of that element is heavier than one-twelfth the mass of one atom of carbon-12.

\(\scriptsize Relative \: Atomic\: Mass = \normalsize \frac{mass \: of \: 1 \: atom \: of \: the\: element }{\frac{1}{12} \: \times \: mass \: of \:1\: atom \: of \: Carbon-12 } \)

From the definition,

1 carbon atom has a mass of 12

1 oxygen atom has a mass of 16

1 hydrogen atom has a mass of 1

The relative atomic mass of an element which exhibits Isotopy is the average mass of its various isotopes.

Relative atomic mass is not a whole number because of the existence of an isotope.

Example 6.4.1:

A natural occurring Chlorine contains 75% of \( \scriptsize _{17} ^{35} \textrm {Cl} \) and 25% of \( \scriptsize _{17} ^{37} \textrm {Cl} \)

Calculate the relative atomic mass of Chlorine.

Solution:

⇒ \( \left( \frac{75}{100} \: \times \: \frac{35}{1} \right) \: +\: \left( \frac{25}{100} \: \times \: \frac{37}{1} \right)\\ \scriptsize = 26.25 \: + \: 9.25\\ \scriptsize = 35.5 \)

Example 6.4.2:

An element x has two Isotopes of \( \scriptsize _{10} ^{20} \textrm {X} \) and \( \scriptsize _{10} ^{22} \textrm {X} \) in the ratio of 1:3. 

What is the relative atomic mass of X?

Solution:

Add ratio (1:3), 1 + 3 = 4

⇒ \( \left( \frac{1}{4} \: \times \: \frac{20}{1} \right) \:+\: \left( \frac{3}{4} \: \times \: \frac{22}{1} \right)\\ \scriptsize = 5 \: + \: 16.5 \\\scriptsize = 21.5 \)

Example 6.4.3:

Natural-occurring Lithium consists of two isotopes of 7.4% of \( \scriptsize _{33} ^{6} \textrm {Li} \)and 92.6% of \( \scriptsize _{33} ^{7} \textrm {Li} \)

Determine the relative atomic mass of Lithium

Solution:

⇒ \( \left( \frac{7.4}{100} \; \times \; \frac{6}{1} \right) \;+\; \left( \frac{92.6}{100} \; \times \; \frac{7}{1} \right)\\ \scriptsize = 0.444 \; + \; 6.483 \\ \scriptsize = 6.926 \)