One advantage of the quantum dot is that, compared to many other fluorescent materials, excited states have relatively long lifetimes (10 ns). What does this mean for the spread in the energy of the photons emitted by quantum dots?

(a) Quantum dots emit photons of more well-defined energies than do other fluorescent materials.

(b) Quantum dots emit photons of less well-defined energies than do other fluorescent materials.

(c) The spread in the energy is affected by the size of the dot, not by the lifetime.

(d) There is no spread in the energy of the emitted photons, regardless of the lifetime.

A quantum dot is a type of crystal so small that quantum effects are significant. One application of quantum dots is in fluorescence imaging, in which a quantum dot is bound to a molecule or structure of interest. When the quantum dot is illuminated with light, it absorbs photons and then re-emits photons at a different wavelength. This phenomenon is called fluorescence. The wavelength that a quantum dot emits when stimulated with light depends on the dot’s size, so the synthesis of quantum dots with different photon absorption and emission properties may be possible. We can understand many quantum-dot properties via a model in which a particle of mass M (roughly the mass of the electron) is confined to a two-dimensional rigid square box of sides L. In this model, the quantum-dot energy levels are given by E_{m, n} = (m² + n²)(π²ℏ²)/2ML², where m and n are integers 1, 2, 3, ....