Quantum Numbers
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1) Erwin Schrodinger developed quantum mechanics and formulated the Schrodinger equation in 1926, which treats electrons as waves rather than particles. 2) The Schrodinger equation led to the discovery of quantum numbers that describe electron behavior and allowed for a more accurate model of atomic structure. 3) There are four quantum numbers - the principal quantum number (n) describes the electron shell or energy level, the azimuthal quantum number (l) describes the subshell shape, the magnetic quantum number (m) describes spatial orientation, and the spin quantum number (s) describes electron spin.
Quantum Numbers
- 1. THE QUANTUM NUMBERS & SHAPES OF ORBITALS CHAPTER # 2 ATOMIC STRUCTURE
- 2. DRAWBACKS OF BOHR’S ATOMIC MODEL • Objections were being made on Bohr’s atomic model about: – the movement of electrons in 3D space – spectra of poly electronic atoms. • Bohr’s atomic model failed to justify these objections. Prepared By: Sidra Javed
- 3. Erwin Rudolf Schrödinger o In 1926, Erwin Rudolf Schrödinger, gave the idea that of wave motion of electron o Nobel Prize in Physics in 1933 Prepared By: Sidra Javed
- 4. Schrödinger Equation o He formulated an equation called “the Schrödinger equation”, in which electrons are treated as moving with wave like motion in 3D space around the nucleus. o The solution of Schrödinger Equation gave a set of numerical values. Prepared By: Sidra Javed
- 5. “The Quantum Numbers” o Explained the arrangement and movement of electrons, spectral lines of poly electronic atoms and gave an acceptable model of an atom. Prepared By: Sidra Javed
- 6. The 4 Quantum Numbers - An Electron’s Address oPrincipal Quantum Number (n) oSpecifies the main energy level (orbit) oAzimuthal Quantum Number (l) oInformation about the sub energy level (orbital) oMagnetic Quantum Number (m) oSpatial orientations of an orbital oSpic Quantum Number (s) oSpin movement of electrons Prepared By: Sidra Javed
- 7. Principal Quantum Number (n) o Size & Energy of an orbit/shell o n=1, 2, 3, 4,…. o Greater value of n represents Bigger orbits with high energies o Distance from the nucleus also increases. Prepared By: Sidra Javed
- 8. Principle Quantum Number (n) Total No. of Electrons in an orbit = 2n2 Value of n Name of Shell Total No. of Electrons 2n2 n=1 K 2(1)2 = 2 n=2 L 2(2)2 = 8 n=3 M 2(3)2 = 18 n=4 N 2(4)2 = 32 Prepared By: Sidra Javed
- 9. Azimuthal Quantum Number (l) o Each energy level is divided into sub levels. o l defines the shape of sub energy level/orbital l Sub level Name No. of electrons 0 s Sharp 2 1 p Principal 6 2 d Diffused 10 3 f Fundamental 14 Prepared By: Sidra Javed
- 10. Relationship between n & l l = 0 (n-1) Orbit n l Orbitals No. of electrons K 1 0 1s 2 L 2 0, 1 2s, 2p 2+6 = 8 M 3 0, 1, 2 3s, 3p, 3d 2+6+10= 18 N 4 0, 1, 2, 3 4s, 4p, 4d, 4f 2+6+10+14=32 Prepared By: Sidra Javed
- 11. n=1 , K shell n=2 , L shell n=3 , M shell n=4 , N shell 1s (2 electrons) 2s (2 electrons) 2p (6 electrons) 3s (2 electrons) 3p (6 electrons) 3d (10 electrons) 4s (2 electrons) 4p (6 electrons) 4d (10 electrons) 4f (14 electrons) IncreasingEnergy&Size Prepared By: Sidra Javed n l
- 12. Magnetic Quantum Number (m) o Explains the effect of an orbital in magnetic field i.e. the orientation of an orbital o Orbitals split up into degenerate orbitals (having same energy & size) in a magnetic field o Each degenerate orbital can hold up to 2 electrons Prepared By: Sidra Javed
- 13. Relationship between l & m m = -l 0 +l l m Degenerate orbitals No. of electrons l = 0, s 0 1 2 l = 1, p -1, 0, +1 3 2+2+2 = 6 l = 2, d -2, -1, 0, +1, +2 5 2+2+2+2+ 2 = 10 l = 3, f -3, -2, -1, 0, +1, +2, +3 7 2+2+2+2+ 2+2+2 = 14 Prepared By: Sidra Javed
- 14. n=1 , K shell n=2 , L shell n=3 , M shell n=4 , N shell l=0, 1s l=0, 2s l=1, 2p l=0, 3s l=1, 3p l=2, 3d IncreasingEnergy&Size Prepared By: Sidra Javed m=0 m=0 m=0 m=0 m=-1 m=+1m=0 m=-1 m=+1m=0 m=-1 m=+1m=0 m=-1 m=+1m=0m=-2 m=+2 m=-1 m=+1m=0m=-2 m=+2 m=-1 m=+1m=0m=-2 m=+2m=-3 m=+3 l=0, 4s l=1, 4p l=2, 4d l=3, 4f n l m
- 15. Spin Quantum Number (s) o Direction of spin of an electron o Electron which rotates around the nucleus also rotates around its own axis o This is called self rotation o Either Clockwise (50%) or anticlockwise (50%) o s = -1/2 (↑) for clockwise o s = +1/2 (↓) for anticlockwise Prepared By: Sidra Javed
- 16. Spin of electron Associated with magnetic field Prepared By: Sidra Javed
- 17. Orbital Diagrams o We often represent an orbital as a square and the electrons in that orbital as arrows. o The direction of the arrow represents the spin of the electron. Orbital with 1 electron Unoccupied orbital Orbital with 2 electrons Prepared By: Sidra Javed
- 18. Prepared By: Sidra Javed IncreasingEnergy 1s2 2s2 3s2 4s2 2p6 3p6 4p6 3d10 4d10 4f14 K shell N shell M shell L shell
- 19. Orbit o The circular path of an electron around the nucleus is called an orbit. o The orbit or shells are denoted by K, L, M, N etc Prepared By: Sidra Javed
- 20. Electron Cloud A cloud showing the probability of finding the electron in terms of charged cloud around the nucleus is called Electron Cloud. Prepared By: Sidra Javed
- 21. Atomic Orbitals: s, p, d, f o Atomic orbitals are regions of space where the probability of finding an electron about an atom is highest. o s orbital spherical shape o p orbital dumb-bell shape o d orbital clover leaf shape o f orbital double clover leaf Prepared By: Sidra Javed
- 22. s orbital - spherically symmetric l= 0 and m = 0 Prepared By: Sidra Javed
- 23. p orbital - dumbbell shaped l = 1 m = -1,0,+1 Prepared By: Sidra Javed
- 24. d orbital shapes l= 2 m = -2,-1,0,+1,+2 Prepared By: Sidra Javed
- 25. f orbital shapes l = 3 m = -3,-2,-1,0,+1,+2, +3 Prepared By: Sidra Javed
- 26. The End Prepared By: Sidra Javed