Nanomaterials And Their Applications

Step 1: Understanding the dimensions.
Given that the side length of the cube is 1 m, we can calculate the number of smaller cubes (each side 1 nm) that can be carved from it.
Since , the volume of the large cube is .
Thus, the number of cubes with side 1 nm is .

Step 2: Calculating the collective surface area.
The surface area of each small cube is .
For the entire collection of cubes, the total surface area is .
Converting this to km²:
Final Answer:

Gold nanoparticles are widely used in clinical diagnostics due to their strong optical properties, such as high absorbance and scattering, which are useful for optical imaging techniques. They also exhibit good fluorescence properties and can be easily functionalized for use in diagnostics, making them the most efficient for clinical applications.
Final Answer:

Step 1: Identifying challenges with carbon nanotubes.
The large-scale use of carbon nanotubes faces several issues:
- (A) Synthesizing carbon nanotubes in pure forms is challenging.
- (B) Dispersion in solvents is difficult due to their strong tendency to clump together.
- (C) Reducing their length is necessary for certain applications but is hard to achieve consistently.
- (D) Tailoring their orientation is essential for specific applications, but this is not always feasible.

Final Answer: