Exercises: Quantum mechanical model

Within quantum mechanics, the concept of orbit in the Bohr model is replaced by that of atomic orbital.

1. a) Define precisely the term "atomic orbital", stating which physical quantity the square of the wave function ($|\psi|^2$) represents.
2. b) State whether knowing the orbital allows the position of an electron to be predicted with certainty before it is measured, and justify your answer by citing the relevant physical principle.

The following illustration shows a two-dimensional cross-section of the dot density corresponding to an atomic orbital of type $s$, highlighting an inner region of high relative density (A) and a peripheral region of lower density (B), bounded by a contour surface. Observe the diagram

and answer the following questions:

1. a) Explain the physical meaning of the dot density in this diagram and justify why a precise circular or elliptical orbit is not drawn in the quantum model.
2. b) Describe what the outer contour line usually shown in textbooks for this type of orbital represents, and explain whether the algebraic signs ($+$ or $-$) that are sometimes assigned to wave functions represent positive or negative electric charge.

You can do it on paper and send a photo with your answer.

Consider the spatial representation and quantum mechanical properties of the atomic orbitals $2p$.

1. a) Describe the three-dimensional geometry of an orbital $2p_z$, stating the number of lobes, the position of its nodal plane and the value of the probability of finding the electron in that plane.
2. b) In graphical representations of the orbitals $2p$, one lobe is usually colored with a positive sign ($+$) and the other with a negative sign ($-$). Explain in detail the physical meaning of these signs, distinguishing it from electric charge, and analyze how this property influences bond formation through in-phase or out-of-phase overlap.