When a hydrogen atom is exposed to a perturbation V = E.z, the first order correction to the wave function comes only from the orbital

Concept:-

Perturbation Theory:

• Perturbation theory is an approximation method to find out the exact solution of any system with great accuracy.
• To break the energy correction in a particular energy level, we have to disturb the operator in a specific order.
• The energy correction is given by,

The perturbed energy levels upto first order are given by,

​

Explanation:-

For a hydrogen atom that is exposed to a perturbation

V= E.z

The orbital which will contribute to the first-order correction to the wave function will be,

​

For 2s, 3p_y, and 3dz2 orbitals the first-order correction to the wave function will be

​,

, and

While for 2p_z orbital, the first-order correction to the wave function will be

​​

As the value of first-order correction to the wave function for 2pz orbital is non-zero, it will contribute to the first-order correction.

Conclusion:-

Hence, the first-order correction to the wave function comes only from the orbital 2pz