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- 1. Electronic configuration of Atom Lecture 7 Week 4
- 2. Wave Mechanics <ul><li>In 1924, de Broglie proposed that if energy is particle like, perhaps matter is wavelike </li></ul><ul><li>According to his theory, e - , p + and even atom, when in motion possessed wave properties and could be associated with λ , ν and А = this is WAVE MECHANICS </li></ul><ul><li>For light: E = h = hc / </li></ul><ul><li>For particles: E = mc 2 (Einstein) </li></ul>L. de Broglie (1892-1987) for particles is called the de Broglie wavelength From previous lecture we know that, Light as well as heat energy exhibits both wave and particle nature under suitable conditions = Wave mechanical theory Therefore, mc = h / and for particles (mass)x(velocity) = h /
- 3. <ul><li>If particle travel in waves, e should exhibit diffraction & interference </li></ul><ul><li>- in 1927, Davisson & Germer guided a beam of electrons at nickel crystal and obtain a diffraction pattern. Ex: see Fig. 7.14 of page 271 of your reference Silberg Chemistry book </li></ul><ul><li>Do a math: </li></ul><ul><li>a) a stone of mass 100gm moving with a velocity 10m/s. What is the de Broglie’s λ for the stone? </li></ul><ul><li>b) an e in H atom has a mass 9.1091×10 -28 gm and moves with a velocity 2.188×10 -8 cm/s. what is the de Broglie’s λ ? </li></ul><ul><li>Wave length of X-rays is 1nm = 1×10 -9 m. </li></ul><ul><li>Compare X-rays λ with de Broglie’s λ . </li></ul>
- 4. Uncertainty Principle <ul><li>If an e has the properties of both a particle and a wave, so we should be able to determine the location of e in the atom. </li></ul><ul><li>In 1927, W. Heisenberg postulated, The Uncertainty principle, which states that it is impossible to know simultaneously the exact position and momentum (velocity) of a particle/ electron . Heisenberg’s relationship is: </li></ul><ul><li>Δ x. m Δ u ≥ h/2 π </li></ul><ul><li>This uncertainty product is negligible in case of large objects </li></ul><ul><li>It means that we can not assign fixed path for e, such as circular orbits of Bohr’s model </li></ul><ul><li>At best we can do is find the probability of finding an e with a probable velocity. </li></ul>W. Heisenberg 1901-1976 So, in macroscopic world, a moving particle has a definite location at any instant and a wave is spread out in space.
- 5. <ul><li>Using this idea, Schrodinger developed a mathematical model based on wave mathematics to describe the position of e in an atom=calculation of the probability of finding e at various points at atom. </li></ul><ul><li>For a given atom, Schrodinger's Equation has many solutions, and each solution is associated with a given wave functions, Ψ , a mathematical description of electron’s motion, also called Atomic Orbital . </li></ul>E. Schrodinger 1887-1961 Ψ does NOT describe the exact location of the electron, but Ψ 2 is proportional to the probability of finding an e- at a given point
- 6. ORBITAL 2 is proportional to the probability of finding an e- at a given point. The three dimensional region within which there is higher probability that an e having certain energy will be found is called ORBITAL, The energy of e in an orbital is always same
- 7. <ul><li>By examining the probabilities given by a particular orbital, a "shape" of the orbital can be seen. This shape represents a space around the nucleus that the electron is most likely to be found. </li></ul><ul><li>The many solutions to Schrodinger's equation can be classified by the shape that is from their probability distributions, called orbital, like s , p , and d-type , as shown above. Most orbital types have several possible orientations too. </li></ul><ul><li>An atomic orbital is specified by three quantum numbers . </li></ul><ul><li>One is related to orbital’s size, another its shape third its orientation in space </li></ul>Quantum number of an atomic Orbital
- 8. Those are principal ( n ) , angular ( l ) , and magnetic ( m ) quantum numbers n l m principal 1, 2, 3, … size and energy angular momentum 0, 1, 2, …, ( n - 1) shape magnetic - l , …, l orientation
- 9. Quantum number of an atomic Orbital <ul><li>Those are the principal ( n ) , angular momentum( l ) , and magnetic ( m ) quantum numbers. </li></ul><ul><li>The principle quantum number (n): </li></ul><ul><li>It actually denotes the principal shell/energy level to which electrons belongs at the atom. It represents the avg. size of atom. Incase of H atom it represents the only orbital of it . </li></ul><ul><li>n is a positive integer (1,2,3,…….7) </li></ul><ul><li>In n’th energy level, atom can have only 2n 2 number of electrons </li></ul>Principal quantum number (n) 1 2 3 4 Max. number of electrons in n’th shell/level 2 8 18 32
- 10. n = 1 l = 0 = (1s) n = 2 l = 0, 1 = (2s, 2p) n = 3 l = 0, 1, 2 = (3s, 3p, 3d) n = 4 l = 0, 1, 2, 3 = (4s, 4p, 4d, 4f) designated by letters l = 0 s orbital l = 1 p orbital l = 2 d orbital l = 3 f orbital Angular momentum quantum number ( l ) It is an integer from 0 to (n-1) It is related to the shape of the orbital
- 11. n = 1 l = 0 m = 0 n = 2 l = 0 m = 0 l = 1 m = -1 m = 0 m = 1 n = 3 l = 0 m = 0 l = 2 l = 1 m = -1 m = 0 m = 1 m = -2 m = -1 m = 0 m = 1 m = 2 s s p s p d 1 1 3 3 1 5 Magnetic quantum number ( l ) It is an integer from –l through 0 to +l It is prescribes the orientation of the orbital in space around nucleus
- 12. <ul><li>For, n = 1 , l = 0 and m = 0 </li></ul><ul><li>There is only one subshell and that subshell has a single orbital </li></ul><ul><li>(m has a single value ---> 1 orbital) </li></ul><ul><li>This subshell is labeled s and we call this orbital 1s </li></ul><ul><li>Each shell has 1 orbital labeled s. </li></ul><ul><li>It is SPHERICAL in shape. </li></ul><ul><li>An atomic orbital is defined by 3 quantum numbers: </li></ul><ul><ul><li>n l m </li></ul></ul><ul><li>Electrons are arranged in shells and subshells of ORBITALS . </li></ul><ul><li>n shell </li></ul><ul><li>l subshell </li></ul><ul><li>m designates an orbital within a subshell </li></ul>Shells and Subshells
- 13. p Orbital & d Orbital <ul><li>For n = 3, </li></ul><ul><li>what are the values of l? </li></ul><ul><li>l = 0, 1, 2 </li></ul><ul><li>and so there are 3 subshells </li></ul><ul><li>in the shell. </li></ul><ul><li>For l = 0, m l = 0 </li></ul><ul><li> s subshell with single orbital </li></ul><ul><li>For l = 1, m l = -1, 0, +1 </li></ul><ul><li> p subshell with 3 orbitals </li></ul><ul><li>For l = 2, </li></ul><ul><li>m l = -2, -1, 0, +1, +2 </li></ul><ul><li> d subshell with 5 orbitals </li></ul><ul><li>For, n = 2, l = 0 and 1 </li></ul><ul><li>There are 2 types of orbitals </li></ul><ul><li>— 2 subshells </li></ul><ul><li>For l = 0 m l = 0 </li></ul><ul><li>this is a s subshell </li></ul><ul><li>For l = 1 m l = -1, 0, +1 </li></ul><ul><li>this is a p subshell with 3 orbitals </li></ul>
- 14. 1 s orbital spherical Shape of Atomic Orbital See Fig-7.17 of Silberg Chemistry Page 278
- 15. Shape of 2p Orbital dumbbell shape 3 p , 4 p , 5 p etc. are similar shapes but larger size
- 16. n = 3, l = 1 Orbitals (3p x 3p y 3p z )
- 17. 3 d orbitals cloverleaf larger n same shapes but size larger
- 18. Representation of 4f Orbitals
- 19. There are n 2 orbitals in the n th SHELL Also see Fig - 7.17 & Fig - 7.18 & Fig – 7.19 and Fig - 8.9of your reference Silberg Chemistry Book 2 1 3d n= 3
- 20. Spin Quantum Number ( s ) <ul><li>The spin quantum value indicates that the electron is spinning on its axis in one direction (clockwise/anti clockwise) or the opposite. </li></ul><ul><li>It can have a value of -1/2 or +1/2 only </li></ul><ul><li>The value of s does not depend on any other quantum number </li></ul><ul><li>These spins are also designated by arrows pointing upwards and downwards as </li></ul>
- 21. Do this math <ul><li>Which of the following sets of quantum numbers are not allowable and why? </li></ul><ul><li>a) n= 2, l=2, m=0, s=+1/2 </li></ul><ul><li>b) n=2, l=0, m=-2, s=-1/2 </li></ul><ul><li>c) n=3, l=2, m=+2, s=-1/2 </li></ul><ul><li>What designation are given to the following orbital? </li></ul><ul><li>a) n=4, l=3 </li></ul><ul><li>b) n=5, l=0 </li></ul><ul><li>c) n=2, l=1 </li></ul><ul><li>Write the missing quantum numbers & sublevel names </li></ul>n l m name a) ? ? 0 4p b) 2 1 0 ? c) 3 2 -2 ? d) ? ? ? 2s
- 22. Pauli’s exclusion principle <ul><li>In 1925, Wolfgang Pauli discover the principle that governs the arrangements of electrons in many electron atoms </li></ul><ul><li>The Pauli exclusion principle states that no two electrons in an atom can have the same set of four quantum numbers n, l, m, s. </li></ul><ul><li>For a given orbital, thus e value of n, l,m are fixed </li></ul><ul><li>Thus if we want to put more than one e in an orbital and satisfy the Pauli exclusion principle, our only option is to assign different values of s to those two e </li></ul><ul><li>We know that their can be only two s value possible for e </li></ul><ul><li>We conclude that, an orbital can hold a max. of two e, and they must have opposite spin. </li></ul>
- 23. Example of Pauli’s Exclusion Principal: <ul><li>Consider the second shell (n=2) </li></ul><ul><li>There are 4 orbitals, one s orbital (l=0) and three p orbitals (l=1) </li></ul>2 e are in 2s orbital 2 e are in 2p x orbital 2 e are in 2p y orbital 2 e are in 2p z orbital n l m s 2 0 0 +1/2 2 0 0 -1/2 2 1 +1 +1/2 2 1 +1 -1/2 2 1 -1 +1/2 2 1 -1 -1/2 2 1 0 +1/2 2 1 0 -1/2
- 24. Electronic configuration No of e in sub shell Electronic configuration of shell 1s 2 2s 2 2p 6 3s 2 3p 6 3d 10 4s 2 4p 6 4d 10 4f 14 2 10 6 14 10 2 2 6 6 2
- 25. Rules of electronic configuration of atom <ul><li>Each e shell can hold max. 2n 2 electrons </li></ul><ul><li>Pattern of e entering in shell: </li></ul><ul><li>1 2 3 4 5 6 7 </li></ul><ul><li>Pattern of e entering in subshell: </li></ul><ul><li>s p d f </li></ul><ul><li>Entering of e in orbital/ Hund’s rule: </li></ul><ul><li>Electrons are distributed among the orbitals of a subshell in such a way as to give the max. number of unpaired e and have the same direction of pair </li></ul>
- 26. <ul><li>Aufbau or Building up rule </li></ul><ul><li>Electrons tend to occupy the available orbitals in increasing order of energies, the orbital of lower energy being filled first. This is building up/Aufbau principle </li></ul><ul><li>The energy of an orbital is determined by the sum of principle quantum number (n) & the angular quantum number (l), this is (n+l) rule </li></ul><ul><li>If in case of two orbital having the same (n+l) value, the orbital with with lower value of n has lower energy. </li></ul>Rules of electronic configuration of atom <ul><li>(n+l) rule </li></ul>
- 27. The relation between orbital filling and the periodic table
- 28. Write electron configuration of the following elements <ul><li>O (8) = ? </li></ul><ul><li>K (19) = ? </li></ul><ul><li>Cl (17) = ? </li></ul><ul><li>Fe (26) = ? </li></ul><ul><li>Zn (30) = ? </li></ul><ul><li>Pb (82) = ? </li></ul>
- 29. Electron configurations in the first three periods.
- 30. Orbital occupancy for the first 10 elements, H through Ne.
- 31. Hund’s rule
- 34. A periodic table of partial ground-state electron configurations
- 35. Assignment 1 <ul><li>Questions number 5, 9, 12, 16 & 23 to 33 . </li></ul><ul><li>Among these 14 questions answer any 7 questions </li></ul><ul><li>Clearly write your name & ID no in the front cover of your assignment sheet </li></ul><ul><li>You can submit the assignment in hand written or as printed form, as you like </li></ul><ul><li>Last date of submission of Assignment 1 is November 15, 2008. </li></ul><ul><li>If anyone submit the Assignment 1 before November 8, 2008 then he/she will be given Bonus 2 marks at the final </li></ul><ul><li>If anyone answers all 14 questions correctly and submit his/her Assignment copy then he/she will be rewarded with Bonus 5 marks at the final </li></ul>Suggestion : Please prepare your notes at least according to the question banks, you can show me your notes, if any correction needed or suggestion then I can give you that.

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