Question

The quantum confinement effect in nanoparticles is observed when:

• A. The particle size is larger than 1 micron
• B. The particle size is smaller than the electron’s de Broglie wavelength
• C. The particle is in a vacuum
• D. The temperature is near absolute zero

Hint:

To identify quantum confinement, remember:
- The particle must be small enough to confine the electrons' wavefunction.
- This occurs when the particle's size is smaller than the electron's de Broglie wavelength.
- Nanoparticles typically exhibit this effect when they are in the size range of 1-100 nm.

Answer 1

The Correct Option is B

The quantum confinement effect refers to the phenomena that occur when a particle is confined to a very small space, typically on the nanoscale. When the particle’s size becomes comparable to or smaller than the de Broglie wavelength of the electrons, quantum effects become significant. This effect is observed in nanoparticles, where the electron's wave-like nature is confined in a small volume, leading to discrete energy levels.
Step 1: Understand Quantum Confinement
In quantum mechanics, the de Broglie wavelength is the wavelength associated with a particle and is inversely related to its momentum. When the particle's dimensions are smaller than the de Broglie wavelength, the particle's behavior can no longer be described by classical physics, and quantum mechanics takes over. This results in discrete energy levels and other quantum phenomena, such as the quantum confinement effect.
Step 2: Analyze Option A - The particle size is larger than 1 micron
The quantum confinement effect is primarily observed in nanoparticles with sizes typically in the range of a few nanometers to around 100 nm, not in particles larger than 1 micron. Larger particles do not exhibit the quantum confinement effect as their size is too large for quantum effects to dominate.
Thus, option A is incorrect.
Step 3: Analyze Option B - The particle size is smaller than the electron’s de Broglie wavelength
This is the correct condition for quantum confinement. When the particle size becomes smaller than the de Broglie wavelength of the electron, quantum effects, such as discrete energy levels, become important. The electron is confined within a small space, and its behavior is governed by the principles of quantum mechanics.
Thus, option B is correct.
Step 4: Analyze Option C - The particle is in a vacuum
While particles in a vacuum can exhibit quantum effects, the quantum confinement effect is more related to the size of the particle, not the external environment like a vacuum. A vacuum does not directly cause quantum confinement; it’s the size of the particle relative to the de Broglie wavelength that matters.
Thus, option C is incorrect.
Step 5: Analyze Option D - The temperature is near absolute zero
Although low temperatures can affect the behavior of nanoparticles, the quantum confinement effect is not directly related to temperature. The critical factor is the particle size, not the temperature. Quantum effects can occur at various temperatures, as long as the particle size is sufficiently small.
Thus, option D is incorrect.