Chapter 5, Problem 93A

Interpretation Introduction

Interpretation:

The diameter of a carbon atom in $\text{μm}$ is to be determined.

Concept Introduction: In chemistry, dimensional analysis is a methodical approach to problem-solving that finds correlations between various units of measurement.

Answer to Problem 93A

  $\text{7}\text{.7}\times {\text{10}}^{-5}\text{μm}$

Explanation of Solution

Conversion factors are as shown:

  $\text{1 pm = 1}\times {\text{10}}^{-12}\text{m}$

  $\text{1 μm = 1}\times {\text{10}}^{-6}\text{m}$

Convert $\text{77 pm}$ into m.

  $\begin{array}{c}\text{77 pm = 77 pm}\times \frac{\text{1}\times {\text{10}}^{-12}\text{m }}{\text{1}\text{pm}}\\ \text{= 7}\text{.7}\times {\text{10}}^{-11}\text{m}\end{array}$

Now $\text{7}\text{.7}\times {\text{10}}^{-11}\text{m}$ into $\text{μm}\text{.}$

  $\begin{array}{c}\text{7}\text{.7}\times {\text{10}}^{-11}\text{m = 7}\text{.7}\times {\text{10}}^{-11}\text{m }\times \frac{\text{1 μm }}{\text{1}\times {\text{10}}^{-6}\text{m}}\\ =\text{7}\text{.7}\times {\text{10}}^{-5}\text{μm}\end{array}$

Conclusion:

The diameter of a carbon atom is $\text{7}\text{.7}\times {\text{10}}^{-5}\text{μm}$