Question

Arrange the following nanomaterials in the order of increasing degree of freedom

(A) Bulk material
(B) Graphene Sheet
(C) Quantum Dot
(D) Carbon Nanotubes
Choose the correct answer from the options given below:

• A. (C), (D), (B), (A).
• B. (A), (B), (C), (D).
• C. (B), (A), (D), (C).
• D. (C), (B), (D), (A).

Hint:

Quantum dots have the highest confinement (3D), while bulk materials have the least (unconstrained).

Answer 1

The Correct Option is A

Step 1: Understand the degree of freedom.
- Bulk material: Has the least degree of freedom since it has continuous translational, vibrational, and rotational freedom at the macroscopic level.
- Graphene sheet: Free to move in two dimensions (2D) but constrained in one.
- Carbon Nanotubes: Have both translational freedom and some unique properties in 1D, offering higher freedom than graphene.
- Quantum Dots: These are confined in all three dimensions, restricting the movement of electrons, which gives them the highest degree of freedom in terms of quantum mechanics.
Step 2: Conclusion.
Thus, the order of increasing degree of freedom is: \[ \text{Quantum Dot (C)}<\text{Carbon Nanotubes (D)}<\text{Graphene Sheet (B)}<\text{Bulk Material (A)} \]
Final Answer: \[ \boxed{\text{(C), (D), (B), (A)}} \]