Session 5.pptx, chemistry, quantum numbers

chemistry

1. Lecture: 5 Concepts of Quantum Numbers Delivered by Dr Deepak Kumar

2. Intended Learning Outcomes At the end of this session students will be able to: Explain different quantum numbers Discuss the significance of each quantum numbers

3. Quantum Numbers On solving Schrödinger wave equation for hydrogen atom we get a number of wave functions These wave functions are characterized by three quantum numbers Can be defined as "the sets of numerical values which give acceptable solutions to the Schrödinger wave equation for hydrogen atom Quantum numbers describe specifically: Energy levels of electrons in atoms Angular momentum, spin, etc.

4. Types of Quantum Numbers Quantum numbers are needed to describe the distribution and position of electrons in an atom First three of them (n, l, m l ) describe the size, shape, and spatial orientation of the probability density distribution of electrons

5. Principal Quantum Numbers Defines the energy level or shell of the electron First quantum number Defines the available values for all other quantum numbers Values of n can be 1, 2, 3, 4 … These are corresponding to electron shells K, L, M, N …..

6. Principal Quantum Numbers Value of n determines the size or distance of the shells from the nucleus Number of electrons in a shell = 2n 2 Number of electrons in K shell (n =1)= 2 since 1 2 = 2, L shell (n =2) 8 since (2. 2 2 )

7. Azimuthal Quantum Numbers Also known as angular momentum quantum number Denoted by l and defines the shape of the orbital Signifies subshell or electron orbital: s, p, d, f Second quantum number to be determined as its value relies only on n

8. Azimuthal Quantum Numbers Value of l decides the shape of the orbital s orbital (l = 0) – spherical, p (l = 1) – polar or dumbbell shaped, d (l =2 ) – double-dumbbell shaped Sharp, principal, diffuse, and fundamental

9. Magnetic Quantum Numbers (m l ) Defines the orientation of the orbital in which the electron inhabits Determines the number of energy states in each orbital which depends on the value of l Number of m l values is called degeneracy, or the number of orbitals in atom that are at the same energy level

10. Magnetic Quantum Numbers (m l ) m l Can take values from – l to + l Only one state for the s orbital ( l = 0), as m l can take only one value (0) In general no. of states = 2 l +1

11. Spin Quantum Numbers ( m s ) Each electron is associated with spin moment Fourth quantum number, m s is related to spin moment of electrons Can have only two values, + ½ and – ½ Completely independent of the values of n, l, and ml

12. Summary