Question

Quantum confinement effects become significant when the size of the particle is comparable to the

• A. \( \text{Wavelength of visible light} \)
• B. \( \text{Exciton Bohr radius} \)
• C. \( \text{Mean free path of a gas molecule} \)
• D. \( \text{Grain size of a metal} \)

Hint:

Quantum Confinement begins exactly when: \( \text{Particle Dimension} \le \text{Exciton Bohr Radius} \). This turns continuous bands into discrete energy steps, shifting the material's properties toward those of an isolated atom.

Answer 1

The Correct Option is B

Concept: Quantum confinement describes changes in electronic and optical properties as a material's physical size is reduced below critical thresholds. In a bulk semiconductor, a photo-excited electron and its corresponding hole form a bound pair known as an exciton. The characteristic physical spatial separation distance between this electron and hole is known as the Exciton Bohr Radius (\( a_B \)).

Step 1: Developing the Confinement Condition
When the physical boundaries of a semiconductor nanocrystal (e.g., a quantum dot) are shrunk down until the particle radius \( R \le a_B \), the electron and hole are spatially compressed together. They no longer behave like unconstrained bulk particles; their wavefunctions are forced to conform to a small 3D box potential.

Step 2: Identifying the Consequence
This spatial compression causes the continuous energy bands of the material to split into discrete energy levels, widening its effective bandgap. This effect becomes noticeable precisely when the physical dimensions scale down to match or fall below the Exciton Bohr radius.