Chapter 3.3, Problem 46SP

Interpretation Introduction

Interpretation : The radius in the unit centimeters is to be expressed.

Concept Introduction : An equivalent measurement ratio is referred to as a conversion factor. An effective approach for resolving conversion problems where measurement in one unit is changed to an equivalent measurement in another is dimensional analysis.

Answer to Problem 46SP

The radius of a potassium atom in the unit centimeters is $2.27\times {10}^{-8}\text{cm}$ .

Explanation of Solution

Given information :

The radius of potassium atom is $0.227\text{nm}$ .

It is known that $\text{1}\text{cm}\text{=}{\text{10}}^{\text{7}}\text{nm}$ .

An equivalent measurement ratio is referred to as a conversion factor. An effective approach for resolving conversion problems where measurement in one unit is changed to an equivalent measurement in another is dimensional analysis.

The desired conversion is $\text{nm}\to \text{cm}$ .

The conversion of the radius is given as:

  $\begin{array}{c}0.227\text{nm}\text{=}0.227\cancel{\text{nm}}\times \frac{{10}^{-7}\text{cm}}{1\cancel{\text{nm}}}\left(\because \text{1}\text{cm}\text{=}{\text{10}}^{\text{7}}\text{nm}\right)\\ =0.227\times {10}^{-7}\text{cm}\\ \text{= 2}\text{.27}\times {10}^{-8}\text{cm}\end{array}$

Conclusion

The radius of a potassium atom in the unit centimeters is $2.27\times {10}^{-8}\text{cm}$ .