Question

The density of iron is \[7.87\,g/c{m^3}\]. If the atoms are spherical and closely packed. The mass of the iron atom is \[9.27 \times {10^{ - 26}}{\text{kg}}\]. What is the volume of an iron atom?
A. \[1.18 \times {10^{ - 29}}{{\text{m}}^{\text{3}}}\]
B. \[2.63 \times {10^{ - 29}}{{\text{m}}^{\text{3}}}\]
C. \[1.73 \times {10^{ - 28}}{{\text{m}}^{\text{3}}}\]
D. \[0.53 \times {10^{ - 29}}{{\text{m}}^{\text{3}}}\]

Answer 1

Hint: To calculate the volume of an atom, we need to know the value of the mass and the density of the atom. Density is given as the mass divided by the volume.

Complete step by step solution:
Given that,
Density of iron =\[7.87\,g/c{m^3}\]
Mass of iron atom = \[9.27 \times {10^{ - 26}}{\text{kg}}\].
We know that,
\[{\text{density}} = \dfrac{{{\text{mass}}}}{{{\text{volume}}}}\]
Using the following given value in the above expression we will now calculate the volume of the iron atom.
\[
  {\text{volume}}\,{\text{of}}\,{\text{iron}}\,{\text{atom}} = \dfrac{{{\text{mass}}}}{{{\text{density}}}} \\
  {\text{volume}}\,{\text{of}}\,{\text{iron}}\,{\text{atom}} = \dfrac{{9.29\, \times {{10}^{ - 26}}}}{{7.87 \times {{10}^3}}}{{\text{m}}^{\text{3}}} \\
  {\text{volume}}\,{\text{of}}\,{\text{iron}}\,{\text{atom}} = \,1.18 \times {10^{ - 29}}{{\text{m}}^{\text{3}}} \\
 \]

Therefore, A is the correct option.

Additional information:
Iron has atomic number of 26 and atomic mass of \[55.85\,{\text{g}}{\text{.mo}}{{\text{l}}^{ - 1}}\]. Iron is placed in the d-block and in the fourth period and group six of the periodic table as it is a transition element. The electronic configuration of iron is \[\left[ {{\text{Ar}}} \right]{\text{3}}{{\text{d}}^{\text{6}}}{\text{4}}{{\text{s}}^{\text{2}}}\]. Iron undergoes rusting in the presence of dump air, and it dissolves in dilute acids. Iron exists in the form of ferrite or \[{\alpha } - \]iron form at room temperature. At a temperature of \[910^\circ {\text{C}}\], iron changes into $\gamma$- iron form. Iron is magnetic in nature.
The element iron has many uses. It is used in making alloy steels like carbon steel with that of chromium, tungsten, manganese, nickel and chromium. Iron is used in the manufacturing of bridges, bicycle chains, cutting tools, electricity bridges, rifle barrels etc. In the Haber process, an iron catalyst is used for the production of ammonia. Iron is used in the production of magnets.

Note: Iron is considered to be the 6th common elements that exist in the universe. Iron contains four allotropes which are \[{\alpha } - \]iron, \[{\gamma } - \] iron, \[{\delta } - \]iron and \[{\varepsilon } - \] iron.