Question

If we decrease the size of a quantum dot that contains an electron, what happens to the energy levels?

Answer 1

We will solve this problem using the direct concept related to band gap energy, that is, a band gap is the distance between the valence band of electrons and the conduction band, i. e, the energy range in a solid where no electron states (Electronic state) can exist Mathematically can be described as,

$E_n = \frac{h^2n^2}{8mcR^2}$

Where,

h = Planck's constant

n = Energy level

mc = Effective mass of the point charge

R = Size of the particle

As you can see the energy is inversely proportional to the size of the particle:

$E_n \propto \frac{1}{R^2}$

Therefore if the size is decreased, the amount of energy is increased.