Examkin

Question

Difficulty: HardBiotechnology and Nanotechnology

In bio-imaging applications, semiconductor quantum dots exhibit size-tunable fluorescence due to quantum confinement, wherein decreasing the nanoparticle radius increases its effective electronic energy bandgap, thereby causing the emitted fluorescence spectrum to shift toward longer wavelengths (red-shift).

Answer: Answer

Answer

The statement is False. Decreasing the size of a quantum dot increases its energy bandgap, which results in the emission of higher-energy photons corresponding to shorter wavelengths (a blue-shift), not longer wavelengths.
Quantum dots display quantum confinement when their physical dimensions approach the exciton Bohr radius. Decreasing the particle size widens the energy gap between the valence and conduction bands. By the fundamental relation E=hcλE = \frac{hc}{\lambda}, a larger energy gap produces higher-energy, shorter-wavelength light (blue-shifted emission). Therefore, the assertion that an increased energy bandgap yields longer wavelengths (red-shift) is scientifically incorrect.

Step-by-Step Solution

1
Analyze the relationship between quantum dot physical size and energy bandgap.
As the radius of a semiconductor quantum dot decreases below its exciton Bohr radius, spatial confinement of charge carriers increases, widening the bandgap (EgE_g).
Quantum confinement alters the electronic band structure, causing energy levels to become discrete and expanding the energy gap between the valence and conduction bands.
2
Apply the Planck-Einstein energy-wavelength equation (E=hcλE = \frac{hc}{\lambda}) to relate energy bandgap to emission wavelength.
An increase in bandgap energy (EE) leads to a shorter emitted wavelength (λ\lambda).
Energy and wavelength are inversely proportional; thus, higher photon transition energies correspond to blue-shifted (shorter wavelength) light.
3
Evaluate the statement's conclusion regarding wavelength shift.
The statement incorrectly asserts that an increased energy bandgap causes a shift toward longer wavelengths (red-shift).
A shift toward longer wavelengths implies lower energy emission, which contradicts the established phenomenon of increased bandgap energy in smaller nanoparticles.

Key Concept

Quantum Confinement Effect and Size-Tunable Optical Emission in Quantum Dots
Rate this question

Topics

Biotechnology and Nanotechnology

More questions from this topic