Concept:
Nanomaterials are materials having dimensions approximately in the range:
\[
1\text{ nm to }100\text{ nm}
\]
At nanoscale dimensions, materials exhibit unusual properties because of:
• Quantum confinement effects
• Large surface area to volume ratio
• Increased surface atoms
These effects significantly alter:
• Optical properties
• Electrical properties
• Catalytic properties
• Magnetic properties
Step 1: Examine Statement A carefully.
Statement A says:
“Nanomaterials show tunable band gap energies.”
This statement is correct.
At nanoscale:
• Electronic energy levels change with particle size.
• Quantum confinement becomes important.
Thus, band gap energy changes with nanoparticle size.
Smaller nanoparticles generally possess:
\[
\boxed{
\text{Larger band gap}
}
\]
Hence, nanomaterials indeed show tunable band gap energies.
Therefore, Statement A is correct.
Step 2: Examine Statement B carefully.
Statement B says:
“Nanomaterials offer enhanced catalytic properties compared to their bulk counterparts.”
This statement is also correct.
Reason:
• Nanoparticles possess enormous surface area.
• More atoms remain exposed on the surface.
• Surface atoms participate actively in catalysis.
Therefore catalytic efficiency increases significantly.
Hence, Statement B is correct.
Step 3: Examine Statement C carefully.
Statement C says:
“Nanomaterials have fixed band gap energies.”
This statement is incorrect.
Band gap energies in nanomaterials are not fixed.
They vary with:
• Particle size
• Shape
• Composition
This tunability is one of the most important properties of nanomaterials.
Thus Statement C is false.
Step 4: Examine Statement D carefully.
Statement D says:
“At nanoscale, color will tell you the size or vice-versa.”
This statement is correct.
Nanoparticles exhibit size-dependent optical properties.
For example:
• Gold nanoparticles show different colors for different sizes.
• Quantum dots emit different colors depending upon size.
Thus:
\[
\boxed{
\text{Color and size are related at nanoscale}
}
\]
Hence Statement D is correct.
Step 5: Identify correct statements.
We found:
• A is correct
• B is correct
• C is incorrect
• D is correct
Therefore:
\[
\boxed{
A,\ B,\ \&\ D\ \text{Only}
}
\]
Step 6: Match with the options.
The correct option is:
\[
\boxed{(2)}
\]
Additional Understanding:
Nanotechnology applications include:
• Drug delivery
• Solar cells
• Sensors
• Catalysts
• Quantum dots
The tunable optical and electronic properties make nanomaterials technologically very important.
Final Conclusion:
Correct statements are:
\[
\boxed{
A,\ B,\ \&\ D\ \text{Only}
}
\]
Hence, the correct answer is:
\[
\boxed{(2)}
\]