Question

Estimate the volume, v, of one sodium atom (na) using its metallic radius of 186 pm. express your answer with the appropriate units.

Answer 1

2.70x10^7 pm^3 We will assume that the sodium atom closely approximates a sphere. So the expression for the volume of a sphere is V = 4/3 pi r^3 V = 4/3 pi (186 pm)^3 V = 4/3 pi 6434856 pm^3 V = 26954261.78 pm^3 Round to 3 significant figures, giving 2.70x10^7 pm^3

Answer 2

The volume of one sodium atom with a metallic radius of 186 pm is $\boxed{26965110.857\;{\text{p}}{{\text{m}}^3}}$

Further explanation:

The smallest particle that is the building block of matter is known as an atom. Most of the space in an atom is empty and its mass is concentrated inside a small region called the nucleus.

Protons, electrons, and neutrons are the three subatomic particles that are present in the atom. Electrons revolve around the nucleus in definite orbits.

The measure of the size of the atoms is known as its atomic radius or atomic size and is defined as the distance from the nucleus to the outermost shell that contains the electrons.  

Types of atomic radius:

1. Covalent radius

Half of the internuclear separation between the nuclei of the two single-bonded atoms of the same species is termed as a covalent radius.

2. Van der Waals radius

It is half of the distance between two unbonded atoms when these have balanced electrostatic forces of attraction.

3. Metallic radius

Half of the distance between the nuclei of two atoms in a crystal is called a metallic radius.

Consider the sodium atoms to be spherical. The formula to calculate the volume of spherical sodium atoms is as follows:

${\text{V}} = \frac{4}{3}{\pi }}{{\text{r}}^3}$                                                        …… (1)

Here,

V is the volume of sodium atoms.

r is the radius of the sodium atom.

The value of r is 186 pm.

Substitute this value in equation (1).

$\begin{aligned}{\text{V}}&=\left( {\frac{4}{3}}\right) \times \left( {\frac{{22}}{7}} \right) \times {\left( {{\text{186 pm}}}\right)^3} \\&=\left( {\frac{{88}}{{21}}} \right) \times 6434856\;{\text{p}}{{\text{m}}^3} \\&=26965110.857\;{\text{p}}{{\text{m}}^3} \\ \end{aligned}$

Therefore, the volume of one sodium atom with a metallic radius of 186 pm is $\boxed{26965110.857\;{\text{p}}{{\text{m}}^3}}$

Learn more:

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Answer details:

Grade: Senior School

Subject: Chemistry

Chapter: Solid State

Keywords: volume, sodium atom, 186 pm, radius, metallic radius, atomic radius, 26965110.857 pm3, atomic radius, covalent radius, van der Waals radius.