Question

which of the following orbitals are degenerate 3dxy,4dxy,3dz2,3dyz,4dyz,4dz2

Answer 1

Answer: 3dxy and [tex]3dz^2 [/tex] are degenerate.

4dxy, 4dyz and $4dz^2$ are degenerate.

Explanation:

Degenerate orbitals are those orbitals which have same value of energy.

Principle Quantum Numbers : It describes the size of the orbital and the energy level. It is represented by n. Where, n = 1,2,3,4....

Azimuthal Quantum Number : It describes the shape of the orbital. It is represented as 'l'. The value of l ranges from 0 to (n-1). For l = 0,1,2,3... the orbitals are s, p, d, f...

Energy of orbitals is given by the expression:

$E=\frac{-Z^2hR}{n^2}$

As E depends only on quantum number n, thus orbitals which have same value of n will have same energy.

3dxy and $3dz^2$ with n=3, will have same energy and and are degenerate

4dxy, 4dyz and $4dz^2$ with n=4, will have same energy and and are degenerate