Questions: A crystallographer measures the horizontal spacing between molecules in a crystal. The spacing is 14.74 nm. What is the total width of a crystal in millimeters 10^5 molecules across? Write your answer as a decimal. mm

Solution Steps

First, convert the spacing from nanometers to millimeters. We know that:

\[ 1 \, \text{nm} = 10^{-9} \, \text{m} \]

and

\[ 1 \, \text{mm} = 10^{-3} \, \text{m} \]

Thus, to convert nanometers to millimeters:

\[ 1 \, \text{nm} = 10^{-6} \, \text{mm} \]

So, the spacing of 14.74 nm in millimeters is:

\[ 14.74 \, \text{nm} \times 10^{-6} \, \text{mm/nm} = 0.00001474 \, \text{mm} \]

The total width of the crystal is the product of the spacing between molecules and the number of molecules across:

\[ \text{Total width} = 0.00001474 \, \text{mm} \times 10^{5} \]

\[ = 1.474 \, \text{mm} \]

Final Answer