According to this model, which statement is true about the energy-level spacing of dots of different sizes?

(a) Smaller dots have equally spaced levels, but larger dots have energy levels that get farther apart as the energy increases.

(b) Larger dots have greater spacing between energy levels than do smaller dots.

(c) Smaller dots have greater spacing between energy levels than do larger dots.

(d) The spacing between energy levels is independent of the dot size.

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, ....