Question

When a chunk of wood burns, much more than just smoke is produced. In addition, nanotubes made of pure carbon are formed that have a structure resembling a roll of chicken wire. These nanotubes are stronger than steel, resistant to fire, and make good heat conductors. If a typical carbon nanotube has a diameter of \(1.3 \mathrm{~nm}\), how many nanotubes would need to be laid side by side to construct a bridge \(40.0\) feet wide?

Short answer

9.38 billion nanotubes are needed.

Step-by-step solution

- Convert Feet to Nanometers

First, convert the width of the bridge from feet to nanometers. We know that:1 foot = 0.3048 meters1 meter = 10^9 nanometersSo, 40.0 feet is converted to nanometers as follows:\(40.0 \text{ feet} \times 0.3048 \text{ meters/foot} = 12.192 \text{ meters}\)\(12.192 \text{ meters} \times 10^9 \text{ nm/meter} = 1.2192 \times 10^{10} \text{ nm}\)

- Calculate Number of Nanotubes

Next, find the number of nanotubes needed. Given that each nanotube has a diameter of 1.3 nm, we use the total width in nanometers to find the number of nanotubes.\( \frac{{1.2192 \times 10^{10} \text{ nm}}}{{1.3 \text{ nm/nanotube}}} = 9.38 \times 10^9 \text{ nanotubes}\)

Key concepts

Carbon Nanotubes

Carbon nanotubes (CNTs) are incredibly tiny tubular structures composed entirely of carbon atoms. They have a unique arrangement that looks like rolled-up chicken wire. These structures possess remarkable properties:

• Stronger than steel
• Fire-resistant
• Excellent conductors of heat

Due to these features, carbon nanotubes have a range of applications, from reinforcing materials to electronics and even drug delivery systems in medicine. The exercise focused on bridging a gap using these nanotubes, highlighting their strength and versatility. To comprehend their scale, it's key to understand their diameter, which is only around 1.3 nanometers, smaller than a virus!

Nanotechnology

Nanotechnology involves manipulating material on an atomic, molecular, or supramolecular scale. This technology has applications in numerous fields like medicine, electronics, energy, and materials science. It relies heavily on understanding and utilizing substances on the nanoscale (1-100 nanometers). Nanotechnology is responsible for advances such as targeted cancer therapy, improved battery storage, and stronger, lighter materials.
Within the context of the exercise, the use of carbon nanotubes serves as a prime example of nanotechnology. By using these nanotubes to construct a bridge, the exercise illustrates how nanotechnology’s advanced materials can solve real-world problems by providing exceptional strength and heat resistance in lightweight, compact forms.

Measurement Conversion in Science

In science, converting measurements accurately is crucial for calculations and understanding scales. This exercise required converting feet to nanometers to determine the number of carbon nanotubes needed. Here’s a simplified guide:

• Convert feet to meters: Multiply by 0.3048
• Convert meters to nanometers: Multiply by 10⁹

For example, to convert 40 feet:

• Multiply 40 feet by 0.3048 to get meters:
  40 ft × 0.3048 = 12.192 meters
• Next, convert meters to nanometers: 12.192 meters × 10⁹ = 1.2192 × 10¹⁰ nanometers

This precise conversion is essential to utilize nanotechnology effectively, ensuring materials like carbon nanotubes are applied correctly based on their tiny scale. Accurate conversions allow for optimal use in construction, medical applications, and technology development.