Question

If ‘u’ denotes 1 atomic mass unit. One atom of an element has mass exactly equal to ‘Au’, where A is the mass number of the element. Find A.
A.${\text{A = 1}}$
B.${\text{A = 12}}$
C.${\text{A = 16}}$
D.A can take up any integral value from 1 to 110

Answer 1

Hint: One atomic mass unit is defined as a mass unit which is exactly equal to one twelfth the mass of a carbon – 12 atom. One atomic mass unit is designated by the symbol amu. But, now amu has been replaced by the new symbol ‘u’.

Complete step by step answer:
Earlier, atomic masses were expressed on a scale on which oxygen was assumed to have a value of 16 units. There were, however, two scales in practice. On the chemists scale, the unit for expressing atomic masses was one sixteenth the mass of an average oxygen atom. On the other hand, on the physicist scale, the unit for expressing atomic masses was one sixteenth the mass of an oxygen – 16 atom.
Later on, the oxygen standard was replaced by carbon – 12 isotopes. For this purpose, the mass of stable carbon – 12 isotopes was assigned a mass of exactly 12 atomic mass units. Thus, one atomic mass unit is one – twelfth the mass of one atom of the most stable and common isotope (C – 12) of carbon.
Therefore, $1{\text{u}} = \dfrac{1}{{12}}$ of mass of one carbon – 12 atoms.
If A is equal to 12, then Au is equal to 12 u. Then, we have:
${\text{Au}} = 12{\text{u}} = 1$ of mass of one carbon – 12 atom.
Or, we can say that when A equals to 12, Au exactly equals the mass of one carbon – 12 atom.

So, the correct answer is B.

Note:
While defining atomic mass, the term ‘average’ was used. This is because most elements consist of atoms of more than one mass. In other words they exist in the form of isotopes. The relative atomic mass of each isotope of an element is termed as its ‘isotopic mass’.
For example, chlorine has two isotopes, both of which have atomic number 17 but atomic masses of 35 and 37. They occur in the ratio $3:1$. Hence, the atomic mass of chlorine will be the average of the two atomic masses.
Average atomic mass of chlorine
$
   = \dfrac{{35 \times 3 + 37 \times 1}}{{3 + 1}} \\
   = 35.5 \\
 $