Question

Arrange the following in terms of increasing dimension of quantum confinement of electrons at nanoscale
• Quantum Dot
• Bulk Material
• Quantum Well
• Quantum Wire Choose the correct answer from the options given below:

• A. D $<$ A $<$ C $<$ B
• B. C $<$ A $<$ B $<$ D
• C. B $<$ C $<$ D $<$ A
• D. A $<$ D $<$ C $<$ B

Hint:

Greater the number of confined dimensions, stronger is the quantum confinement effect: \[ \text{Bulk} < \text{Well} < \text{Wire} < \text{Dot} \]

Answer 1

The Correct Option is D

Concept: Quantum confinement refers to the restriction of motion of electrons in one or more spatial dimensions at the nanoscale. As the dimensions available for electron movement decrease, quantum effects become stronger. Different nanostructures confine electrons in different numbers of dimensions:
• Bulk material $\rightarrow$ No confinement
• Quantum well $\rightarrow$ Confinement in one dimension
• Quantum wire $\rightarrow$ Confinement in two dimensions
• Quantum dot $\rightarrow$ Confinement in all three dimensions Thus, increasing confinement means increasing number of confined dimensions.

Step 1: Understand Bulk Material. In bulk material:
• Electrons are free to move in all three dimensions.
• There is practically no quantum confinement. Hence bulk material has: \[ \boxed{ \text{Least confinement} } \]

Step 2: Understand Quantum Well. A quantum well confines electrons in: \[ \boxed{ 1 \text{ dimension} } \] while electrons remain free in the other two dimensions. Hence confinement is greater than bulk material.

Step 3: Understand Quantum Wire. A quantum wire confines electrons in: \[ \boxed{ 2 \text{ dimensions} } \] Electrons can move freely only along one dimension. Thus confinement becomes stronger.

Step 4: Understand Quantum Dot. Quantum dots confine electrons in: \[ \boxed{ 3 \text{ dimensions} } \] Electrons become localized in all directions. Hence quantum dots possess: \[ \boxed{ \text{Maximum quantum confinement} } \]

Step 5: Arrange in increasing order of confinement. Increasing confinement means: \[ \text{Bulk Material} < \text{Quantum Well} < \text{Quantum Wire} < \text{Quantum Dot} \] Using the symbols: \[ B < C < D < A \]

Step 6: Choose the correct option. Thus the correct arrangement is: \[ \boxed{ B < C < D < A } \] Hence the correct option is: \[ \boxed{(3)} \] Final Conclusion: The increasing order of quantum confinement is: \[ \boxed{ \text{Bulk Material} < \text{Quantum Well} < \text{Quantum Wire} < \text{Quantum Dot} } \] Hence, the correct answer is: \[ \boxed{(3)} \]