Question

A crystallographer measures the horizontal spacing between molecules in a crystal. The spacing is 15.93nm. What is the total width of a crystal in millimeters 105 molecules across? Write your answer as a decimal.

Answer 1

0.00167265 mm

Explanation:

Given the spacing between the molecules in the crystal is 15.93 nm.

1 nm = $10^{-9}$ m

so 15.93 nm = 15.93 * $10^{-9}$ = 1.593 * $10^{-8}$ m

Spacing between 2 molecules is  1.593 * $10^{-8}$ m

So total width of 105 molecules crystal is 1.593 * $10^{-8}$ *105 = 167.265 * $10^{-8}$ m

We know that

1 m = 1000 = $10^{3}$ mm

So total width of 105 molecules crystal in millimeters is 167.265 * $10^{-8}$  *$10^{3}$

 = 167.265 * $10^{-5}$ = 1.67265 * $10^{-3}$ mm = 0.00167265 mm