Question

The model, particle in box can be used to estimate the energy of spectral transition in the molecules. (Justify the statement)

Answer 1

In an atom ,as we know, the electrons are revolve around the nucleus.According to quantum mechanics each electrons are associated with a wave function.That is, if the wave function of an electron is means the electron belongs to the nth orbital having energy En. As in particle a box when a photon of particular frequency incident on atom or molecule, the atom or molecule goes to higher energy level. i.e the electrons moves from one electronic state to another. This change is known as transtion.This is similar to a praticle in a box is excited to higher energy level.

When a photon is incident on an atom the electron get excited.

the change in energy of this transition is

For a particle in a box the energy of a particular state is given by

the change in energy is

i.e

For the molecules considered in transitions, the electronic energy level spacing corresponds to the energy of a visible photon. Specifically, there must be high-energy valence electrons capable of traveling "freely" over the length of the molecule, L. These "free" electrons behave approximately like the particles in a one-dimensional box.As L becomes very large the energies get closer and closer together, eventually becoming continuous (no longer “quantum”); this is due to L being much larger than wavelength λ for a particle with a typical energy. Similarly, increasing the mass has the same qualitative effect as making the box larger, which is why you (a “particle”) do not notice quantum effects when you sit in a room (a “box”), even though your motion is fundamentally described by quantum mechanics. Stated another way, discrete energy level spacing is observed for very lowmass particles confined to small quarters (in this case, an electron within an atom or molecule that gives a small value for mL2 ).