Question

A crystallographer measures the horizontal spacing between molecules in a crystal. The spacing is

Answer 1

Answer: The total width of a crystal is 1.65 mm.

Explanation:

Horizontal length between the two molecules = 16.5 nm

Width of the $10^5$ molecules :$16.5 nm\times 10^5=16.5\times 10^5 nm$

$1 nm=10^{-6} mm$

The total width of a crystal in millimeter=$16.5\times 10^5\times 10^{-6} mm=1.65 mm$

The total width of a crystal is 1.65 mm.

Answer 2

1.65 mm

Further explanation

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,

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

$\boxed{ \ 1 \ mm = 10^{-3} \ m \ }$

Crystallographers observe 10⁵ molecules across with the intermolecular distance in the crystal is 16.5 nm.

$\boxed{ \ 10^5 \ molecules \times \frac{16.5 \ nm}{molecules} \times \frac{10^{-9} \ m}{1 \ nm} \times \frac{1 \ mm}{10^{-3} \ m} =? \ }$

We cross out the same units.

$\boxed{ \ = 10^5 \times 16.5 \times 10^{-9} \times \frac{1 \ mm}{10^{-3}} \ }$

$\boxed{ \ = 16.5 \times 10^{5 - 9 + 3} \ mm \ }$

$\boxed{ \ = 16.5 \times 10^{-1} \ mm \ }$

$\boxed{ \ = \frac{165}{10} \times \frac{1}{10} \ mm \ }$

$\boxed{ \ = \frac{165}{100} \ mm \ } \rightarrow \boxed{\boxed{ \ 1.65 \ mm \ }}$

Thus, the total width of a crystal in millimeters is 1.65 mm.

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