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11 days ago

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

Chemistry

2 answers:

Tems11 [846]11 days ago

7 0

1.65 mm

Further explanation

Given:

A crystallographer observes horizontal spacing among molecules in a crystal, measuring 16.5 nm.

Question:

What is the entire width of a crystal in millimeters accounting for 10⁵ molecules?

The Process:

A conversion of units is necessary here, focusing on length. We will convert nanometers to millimeters this time.

Recall that,

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

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

Crystallographers have identified 10⁵ molecules across with the inter-molecular gap in the crystal at 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 cancel out matching units.

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

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

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

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

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

Consequently, the overall width of a crystal in millimeters is 1.65 mm.

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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

castortr0y [923]11 days ago

7 0

Answer: The overall width of a crystal measures 1.65 mm.

Explanation:

Horizontal distance separating the two molecules is 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 overall width of a crystal measured in millimeters= $16.5\times 10^5\times 10^{-6} mm=1.65 mm$

The overall width of a crystal is 1.65 mm.

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