Answer: The total width of a crystal is 1.65 mm.
Explanation:
Horizontal length between the two molecules = 16.5 nm
Width of the [tex]10^5[/tex] molecules :[tex]16.5 nm\times 10^5=16.5\times 10^5 nm[/tex]
[tex]1 nm=10^{-6} mm[/tex]
The total width of a crystal in millimeter=[tex]16.5\times 10^5\times 10^{-6} mm=1.65 mm[/tex]
The total width of a crystal is 1.65 mm.
1.65 mm
Given:
A crystallographer measures the horizontal spacing between molecules in a crystal. The spacing is 16.5 nm.
Question:
What is the total width of a crystal in millimeters that is 10⁵ molecules across?
The Process:
We will solve the problem of unit conversion, especially the unit of length. This time we will convert nanometers to millimeters.
Recall that,
[tex]\boxed{ \ 1 \ nm = 10^{-9} \ m \ }[/tex]
[tex]\boxed{ \ 1 \ mm = 10^{-3} \ m \ }[/tex]
Crystallographers observe 10⁵ molecules across with the intermolecular distance in the crystal is 16.5 nm.
[tex]\boxed{ \ 10^5 \ molecules \times \frac{16.5 \ nm}{molecules} \times \frac{10^{-9} \ m}{1 \ nm} \times \frac{1 \ mm}{10^{-3} \ m} =? \ }[/tex]
We cross out the same units.
[tex]\boxed{ \ = 10^5 \times 16.5 \times 10^{-9} \times \frac{1 \ mm}{10^{-3}} \ }[/tex]
[tex]\boxed{ \ = 16.5 \times 10^{5 - 9 + 3} \ mm \ }[/tex]
[tex]\boxed{ \ = 16.5 \times 10^{-1} \ mm \ }[/tex]
[tex]\boxed{ \ = \frac{165}{10} \times \frac{1}{10} \ mm \ }[/tex]
[tex]\boxed{ \ = \frac{165}{100} \ mm \ } \rightarrow \boxed{\boxed{ \ 1.65 \ mm \ }}[/tex]
Thus, the total width of a crystal in millimeters is 1.65 mm.
Keywords: crystallographer, measures, the horizontal spacing, between, molecules, in a crystal, 16.5 nm, the total width, a crystal, in millimeters, nanometers, 10^5 molecules across, write, your answer, as a decimal, conversion, the unit of length, 1.65
