Question

A crystallographer measures the horizontal spacing between molecules in a crystal. The spacing is
10.59
nm
. What is the total width of a crystal in millimeters
105
molecules across? Write your answer as a decimal.

Answer 1

Answer : $1.101 X 10^{-3}$ mm

Explanation : It is true that when objects are placed in a line with spaced in between them, the number of spaces is one less than the number of objects.

Hence, if there are 105 molecules, there will be 104 spaces present in between these molecules.

As the conversion factor for 1 mm = $1 X 10^{6}$ nm.

Now, converting the spacing to millimeters from nanometers

So, spacing will be = $\frac{10.59}{1 X 10^{6} }$  

∴ Spacing = $1.059 X 10^{-5}$ nm

Now, we know the width of the lattice will be

= 104 X $1.059 X 10^{-5}$ =$1.101 X 10^{-3}$ mm