ATOMIC ORBITALS, BONDS AND DISPERSION FORCES You may have seen pictures of atomi

Question

ATOMIC ORBITALS, BONDS AND DISPERSION FORCES

You may have seen pictures of atomic orbitals such as those above. The color represents the phase or sign of the orbital. What these pictures do not show is that such orbitals are not static, they are dynamic structures.

Each orbital has a certain energy value in a given atom. Let?s see what that implies about the orbital. The Schr?dinger equation is

The left and center expressions form the equation which is solved to find the energy and wave function for each orbital. The center and right expressions hold the information we are after. Assume:

then the left equation yields the expressions for

and E_nl. Using that value for E, the right equation gives:

Consider the following equation:

The solution to this equation, using the relation

is:

Suppose two hydrogen atoms are close to one another. If they get close enough, the waves represented by the orbitals overlap. When two waves are at the same location at the same time they experience superposition and add together.

PROBLEM STATEMENT

There are two cases for the overlap of the two waves: 1) The waves have the same sign where they overlap, and 2) The waves have opposite signs where they overlap.

For each case, use superposition to get the amplitude of the waves halfway between the hydrogen nuclei and identify which case will lead to a stable comination of orbitals and atoms (Keeping Coulomb?s law in mind)?

Explanation / Answer

answer : 1) The waves have the same sign where they overlap will lead to a stable comination of orbitals and atoms

same sign waves result stable combination of atomic orbitals.

if same sign waves overlap with each other the resultant wave amplitude increases. it is constructive interfernce of the waves.

if two different sign waves overlap the resultant wave is nullfied . it is completely destrctive interference.

onething in this question , the bonding formation between two waves based on the probability calculations so here we need apply coulomb's law in my opinion . coulomb's law for charges of two species. here we are taking same atoms atomic orbitals . within the atom we are discusiing the possibility of overlaping capacity of orbitals.

same energy and same phase orbitals always will leads to form new bond .

if phases are different there is no bond . that indicate node.

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