Chapter 4.1, Problem 6LC

Interpretation Introduction

Interpretation : The range of the radii of most atoms in nanometers is to be identified.

Concept Introduction : The smallest component of an element that maintains its identity during a chemical reaction is called an atom. A nanometer is a ${\text{10}}^{-9}\text{m}$ wide unit of spatial measurement.

Answer to Problem 6LC

The range of the radii of most atoms in nanometers is within $\text{0}\text{.05}\text{nm}$ to $\text{0}\text{.2}\text{nm}$ .

Explanation of Solution

Most atoms have radii between $5\times {10}^{-11}\text{m}$ to $2\times {10}^{-10}\text{m}$ .

The range of atoms in meters is supposed to be converted into nanometers.

Conversion of $5\times {10}^{-11}\text{m}$ in nm is given as:

  $\begin{array}{c}{\text{5×10}}^{-\text{11}}\text{m}={\text{5×10}}^{-\text{11}}\cancel{\text{m}}\times \frac{{10}^9\text{nm}}{1\cancel{\text{m}}}\left(\text{1}\text{m}\text{=}{\text{10}}^{\text{9}}\text{nm}\right)\\ \text{=}{\text{5×10}}^{-\text{11+9}}\text{nm}\\ \text{=}{\text{5×10}}^{-2}\text{nm}\\ =0.05\text{nm}\end{array}$

Conversion of $2\times {10}^{-10}\text{m}$ in nm is given as:

  $\begin{array}{c}2\times {10}^{-10}\text{m}\text{=}2\times {10}^{-10}\cancel{\text{m}}\times \frac{{10}^9\text{nm}}{1\cancel{\text{m}}}\left(\text{1}\text{m}\text{=}{\text{10}}^{\text{9}}\text{nm}\right)\\ \text{=}2{\text{×10}}^{-\text{10+9}}\text{nm}\\ \text{=}2{\text{×10}}^{-1}\text{nm}\\ =0.2\text{nm}\end{array}$

The range of the radii of most atoms in nanometers is within $\text{0}\text{.05}\text{nm}$ to $\text{0}\text{.2}\text{nm}$ .