a basic introduction to quantum chemistry by Neha Tunki (Institute Of Science)

1. QUANTUM CHEMISTRY
Hydrogen atom and Quantum numbers
Neha Tunki
02

2. Contents
 Hydrogen Atom
 Two particle problem
 Seperation of energy as transational and rotational
 The R  and  Equations
 Introduction to the four quantum numbers and their interdependence on the
solutions of the three equations

3. Hydrogen Atom
 The Hydrogen atom consists of an electron and a proton.
 We shall assume electron and proton to be point masses whose interactionsis
given by coulomb’s law
 −𝑧𝑒2
/4Π𝜀𝑜𝑟
 Z is the atomic no. ; 𝜀𝑜 is the permittivity of the vaccums
 Since the electron is very much faster than the nuclear particles, it is assumed that
the nucleus is stationary as compared to the electron
 Thus, Schrodinger equation for the hydrogen atom will be the equation for a single
electron moving around the nucleus.
 Thus, [−ℎ2/8Π2me 2
+ V] (x y z) = E(x y z)

4. Separation of variables
 In order to solve the previous given
equation, the Cartesian co ordinates
are converted to r   as,
 X = r sin  cos 
 Y = r sin  sin 
 Z = r cos 
 And 𝑥2
+ 𝑦2
+ 𝑧2
=𝑟2
 The transformation of Cartesian co-
ordinates in equation into spherical
polar co-ordinates gives:

5. Separation of variables

10. Two particle problem

14. Questions
 Use the method of separation of variables to breakup the Schrodinger equation for
a rigid rotor to ordinary angular equation.
 Obtain Radial Wave Equation From the Schrodinger wave equation for spherical co
ordinates
 Justify the terms Principle, Azimuthal and magnetic quantum number for n, L, and
M respectively

15. Reference
 Quantum Chemistry by Ira N. Levine
 Fundamentals of Quantum Chemistry by R. Anantharaman
 Quantum Chemistry by Tamas veszpremi and Miklos Feher

16. THANKYOU..!