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In the December 1999 issue of the journal Science, two Harvard scientists describe a pair of "nanotweezers" they created that are capable of manipulating objects as small as one- 50,000 th of an inch in width. The scientists used the tweezers to grab and pull clusters of polystyrene molecules, which are of the same size as structures inside cells. A future use of these nanotweezers may be to grab and move components of biological cells. a. Express one- 50,000 th of an inch in scientific notation. b. Express the size of objects the tweezers are able to manipulate in meters. c. The prefix "nano" refers to nine subdivisions by \(10,\) or a multiple of \(10^{-9}\). So a nanometer would be \(10^{-9}\) meters. Is the name for the tweezers given by the inventors appropriate? d. If not, how many orders of magnitude larger or smaller would the tweezers' ability to manipulate small objects have to be in order to grasp things of nanometer size?

Step by step solution

01

Express one-50,000th of an inch in scientific notation

One-50,000th of an inch is written as \(\frac{1}{50000}\). To convert to scientific notation, divide 1 by 50,000: \(\frac{1}{50000} = 2 \times 10^{-5}\).

02

Convert the size from inches to meters

First, remember that 1 inch = 0.0254 meters. Therefore, multiply the scientific notation value by 0.0254: \(2 \times 10^{-5} \times 0.0254 = 5.08 \times 10^{-7}\) meters.

03

Check the appropriateness of the name 'nanotweezers'

Since 'nano' means \(10^{-9}\) meters and the size the tweezers can manipulate is \(5.08 \times 10^{-7}\) meters, which is larger than a nanometer, the name 'nanotweezers' is not entirely accurate.

04

Determine the orders of magnitude difference needed

The tweezers manipulate structures of size \(5.08 \times 10^{-7}\) meters. For it to be able to manipulate nanometer size objects, it should be \(10^{-9}\) meters. To find how many orders of magnitude larger this is: \(5.08 \times 10^{-7} \div 10^{-9} = 508\). Therefore, the tweezers need to manipulate objects 508 times smaller, which means by 2 orders of magnitude (\(10^{-7.7} \rightarrow 10^{-9.7})\).

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Key Concepts

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

unit conversion

Understanding unit conversion is key when working with measurements in science, especially when dealing with different systems of units like inches and meters. To convert inches to meters, recall that 1 inch equals 0.0254 meters. This conversion factor allows us to translate measurements from the imperial system to the metric system.

For instance, in the exercise, one-50,000th of an inch needs to be expressed in meters. Since 1 inch is 0.0254 meters, multiplying this by the given fraction (2 x 10^-5) yields the desired measurement in meters. Employing scientific notation, which simplifies computations with very large or very small numbers, helps maintain accuracy and readability in such conversions.

nanotechnology

Nanotechnology involves manipulating matter at the atomic or molecular scale, typically within dimensions less than 100 nanometers. This scale is incredibly small, with a nanometer being one-billionth of a meter (10^-9 meters). This field has numerous potential applications, including medical devices, electronics, and materials science.

The nanotweezers mentioned in the exercise represent a tool that can operate at such small scales, theoretically being capable of grabbing objects as tiny as the components inside biological cells. However, upon solving the exercise, it becomes clear that these tweezers currently work on objects sized at 5.08 x 10^-7 meters, which is somewhat larger than the nanoscale objects implied by their name.

Despite this naming discrepancy, nanotechnology continues to push boundaries, enabling manipulation of objects at scales previously unimaginable, and fostering new advancements in science and technology.

orders of magnitude

Orders of magnitude describe the size or scale of numbers in exponential terms. This concept is useful for comparing vastly different quantities. Each order of magnitude represents a tenfold difference. For example, 10^1 (10) is one order of magnitude larger than 10^0 (1), and 10^-1 (0.1) is one order of magnitude smaller than 10^0.

In the exercise, determining whether the name 'nanotweezers' is appropriate involves understanding orders of magnitude. The tweezers can manipulate objects sized at 5.08 x 10^-7 meters, while a nanometer is 10^-9 meters. Comparing these, the objects are around two orders of magnitude larger than a nanometer.

Improving the tweezers to manipulate true nanoscale objects would require enhancing their capability by two orders of magnitude, making them capable of handling objects in the 10^-9 meter range. This highlights the importance of precision and accuracy in scientific tools and their naming conventions.