VKC ScienceChemistry for written exams Telegram

Indian Forest Service (Mains)

Chemistry optional

  • 2 papers
  • 200 marks each
  • 3 h per paper

Paper I covers physical and inorganic chemistry.

Indian Forest Service (Mains), Chemistry optional · 2025 · Paper I

Q2(a)(i). Hydrogen equation in spherical coordinates

Question

Write the time-independent Schrödinger equation for hydrogen in spherical polar coordinates (r, θ, φ) with origin at the nucleus and a stationary proton. Show the relation to Cartesian coordinates pictorially. What are r, θ, φ called?

Answer in brief

Use the Coulomb potential −e²/(4πε₀r) and the spherical-coordinate Laplacian; r is the radial distance, θ the polar angle and φ the azimuthal angle.

Part of VKC Basic

Read the key points and the full model answer with VKC Basic

VKC Basic (₹999 for 6 months) opens every solved answer, the notes, the handbook and the daily answer archive. Every Mains test series includes it.

See what is included Already a member? Sign in

The full model answer

As written for the answer booklet: the diagram carries the working, the lines stay short. Read here only; it is not offered as a download.

The handwritten model answer pages open with the VKC plan.
Read the whole 2025 solution2025 question paper

Topic notes: the hydrogen atom: Schrödinger equation in spherical coordinates, quantum numbers, radial distribution, nodes and orbital shapes, with every Civil Services, IFoS and Geo-Scientist PYQ →

CoversSchrödinger equation hydrogen atomspherical polar coordinatesLaplacianazimuthal angleseparation of variables

All parts of Question 2