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Chapter 1: Problem 34

Convert \(6743 \mathrm{~nm}\) to (a) \(\AA\) (b) inches (c) miles

Short Answer

Expert verified
Answer: The equivalent lengths of 6743 nm are approximately 67,430 脜, 2.65 x 10^-7 inches, and 4.19 x 10^-12 miles.

Step by step solution

01

Convert nanometers to angstroms

To convert the given length in nanometers to angstroms, multiply the length by the conversion factor of 10. In this case, 6743 nm multiplied by 10 gives us: \[6743 \times 10 = 67430 ~\AA\]
02

Convert nanometers to inches

To convert the given length in nanometers to inches, divide the length by the conversion factor of 25.4 million (25,400,000). In this case, 6743 nm divided by 25,400,000 gives us: \[\frac{6743}{25,400,000} \approx 2.65 \times 10^{-7} ~\text{inches}\]
03

Convert nanometers to miles

To convert the given length in nanometers to miles, divide the length by the conversion factor of 1.609 * 10^12. In this case, 6743 nm divided by 1.609 * 10^12 gives us: \[\frac{6743}{1.609 \times 10^{12}} \approx 4.19 \times 10^{-12} ~\text{miles}\]

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Understanding Nanometers to Angstroms
Nanometers (nm) and angstroms (\(\AA\)) are both units used to measure extremely small lengths. They are particularly important in fields like physics and chemistry, when dealing with atomic and molecular scales. One nanometer is equal to 10 angstroms. So, to convert from nanometers to angstroms, you simply multiply by 10.

Here's how it works: if you have 6743 nm, you calculate it in angstroms as follows:
  • Multiply 6743 by 10
  • Result: 67430 \(\AA\)
This straightforward multiplication step makes the conversion simple and rapid.
Converting Nanometers to Inches
Converting from nanometers to inches might seem tricky, but it becomes simple with the right conversion factor. An inch is quite larger compared to a nanometer, so the conversion requires dividing by a large number. To convert nanometers to inches, we use the factor of 25.4 million (or 25,400,000). This is based on the number of nanometers per inch.

Let's see this with our example of 6743 nm:
  • Divide 6743 nm by 25,400,000
  • Result: approximately \(2.65 \times 10^{-7}\) inches
This conversion highlights how small a nanometer is compared to an inch.
Converting Nanometers to Miles
Miles are even larger units compared to nanometers. When converting nanometers to miles, we deal with an enormous conversion factor. One mile is equivalent to roughly 1.609 trillion (1.609 x 1012) nanometers. This highlights the significant difference in scale.

Using the example of 6743 nm, you perform the conversion as follows:
  • Divide 6743 nm by \(1.609 \times 10^{12}\)
  • Result: approximately \(4.19 \times 10^{-12}\) miles
This conversion shows how minuscule a nanometer is when considered in the context of miles.

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Most popular questions from this chapter

A lap in most tracks that use the English system is \(0.25 \mathrm{mi}\) (English lap). In countries that use the metric system, a metric lap is \(0.50 \mathrm{~km}\). A champion marathon runner covers a mile in about \(5.0 \mathrm{~min}\). How many minutes will the runner take to run an English lap at that speed? A metric lap?

A glass of lukewarm milk is suggested for people who cannot sleep. Milk at \(52^{\circ} \mathrm{C}\) can be characterized as lukewarm. What is the temperature of lukewarm milk in \({ }^{\circ} \mathrm{F}\) ? In \(\mathrm{K}\) ?

The volume of a sphere is \(4 \pi r^{3} / 3\), where \(r\) is the radius. One student measured the radius to be \(4.30 \mathrm{~cm} .\) Another measured the radius to be \(4.33 \mathrm{~cm}\). What is the difference in volume between the two measurements?

A waterbed filled with water has the dimensions \(8.0 \mathrm{ft} \times 7.0 \mathrm{ft} \times\) \(0.75 \mathrm{ft}\). Taking the density of water to be \(1.00 \mathrm{~g} / \mathrm{cm}^{3}\), how many kilograms of water are required to fill the waterbed?

Write the name of the element represented by the following symbols. (a) \(\mathrm{Cr}\) (b) \(\mathrm{Ca}\) (c) Fe (d) \(\mathrm{Zn}\)
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