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Elect

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  • 1. ELECRONIC STRUCTURE OF ATOM
    • Atomic theories/ models of atom:
    • Dalton’s Atomic Theory - All matter made up of tiny indivisible particles called atoms.
    • Thompson’s Atomic Theory - atom is a positively charged ball with electrons scattered within it.
    • Rutherford’s Atomic Theory – atom is made up of a small dense positive mass (nucleus) with e moving in the space around the nucleus of the atom .
    • Bohr’s Atomic Theory
    • Quantum / wave Mechanics
  • 2. Bohr’s Atom Bohr’s Atomic Theory: Explain 1.The stability of atom as opposed to Rutherford’s atomic model. 2. The formation of line spectrum in hydrogen atom.
    • Bohr’s atomic postulates ( For H atom)
    • Electron moves in circular orbit around the nucleus, does not radiate or absorb any energy.
  • 3. 2. The energy at each permitted orbit is quantized (only certain specific quantity is allowed) i.e. energy level with a quantum number, n. Energy of electron at energy level n, E n = - A / n 2 (Bohr equation) where A = Rydberg constant. Note: n = Principle quantum no. ( n = 1, 2, 3…  ) identifies and determines the the orbit and energy of its electron.
  • 4. 3. At its normal condition, a H atom is at its ground state ( lowest energy state where n =1) 3. If energy is supplied, an electron may absorb a certain amount of energy to move to a higher energy state called the excited state. 4. Electron at the excited state (i.e. at a higher energy state, E i ) is unstable , tends to return to a lower energy state ( E f ).
  • 5.
    • In the process, an amount of energy is released as radiant energy (photon, light energy ) given by :
    • E = E f – E i
    • E = - A/ n f 2 – (- A./n i 2 ) = A( 1/n i 2 – 1/n f 2 ) ---( 1)
    • Where A = Rydberg constant
    Planck relates energy of a radiation to its frequency by, E = h  -------------( 2 ) Where h = Planck constant,  = frequency of light
  • 6. Subst. (2) into (1). Then h  = - A/ n f 2 – (- A./n i 2 )  E = A( 1/n i 2 – 1/n f 2 )--------- (i) = E f – E i ----------------------------------------------(ii) Where A = Rch = Rydberg constant = 2.178 x 10 -18 J
  • 7. But velocity of light (radiation), c = λ x  where λ = wavelength &  = frequency Hence, E = h x (c/ λ ) Planck relates energy of a radiation to its frequency by, E = h  Where h = Planck constant,  = frequency of light Planck Equation:
  • 8.
    • e.g. Calculate
    • the energy of an electron at energy level n = 2 and when it’s elevated to n = 4. [ Rydberg constant, A = 2.18 x 10-18 J ]
    • The energy given out when the electron translates from the energy level, n = 4 to n = 2.
    • The frequency and wavelength of the radiation emitted in ii. above.
    • State the energy required to elevate an electron from energy level,
    • n =2 n = 4.
  • 9. i. Energy of an electron E 2 = - 2.18 x 10 -18 J / 2 2 = -5.45 x 10 -19 J E 4 = - 2.18 x 10 -18 J / 4 2 = -1.36 x 10 - 19 J ii. Energy given out Δ E = E f – E i = E 2 – E 4 = -5.45 x 10 -19 J – (-1.36 x 10 -19 J) = - 4.09 x 10 -19 J ANS:
  • 10.
    • iii. The frequency(  ) and wavelength( λ ) of the radiation
    • = E/h = 4.09 x 10 -19 J /6.63 x 10 -34 J-s = 6.17 x 10 14 s -1
    • λ = c/  = 3.00 x 10 8 m/s / 6.17 x 10 14 s -1 = 4.86 X 10 -7 m
    iv. energy required for e translation, n =2 n = 4. = 4.09 x 10 -19 J
  • 11. e.g. 2. Find the a quantum of energy of orange light having a frequency of 4.92 x 10 14 s -1 . What is the wavelength of the light? By Planck equation, E = h  = 6.634 x 10 -34 J-s x 4.92 x 10 14 s -1 = 3.264 x 10 -19 J Using velocity of light c = λ  , wavelength λ = c /  = 3.00 x 10 8 m/s / 4.92 x 10 14 s -1 = 6.098 x 10 -7 m ANS:
  • 12. Exercise: 1. An electron in a H atom is excited from energy level n= 1 to energy level n= 5.[Rydberg constant, A = 2.18 x 10-18 J, ] Calculate : a) energy of electron at energy levels, n= 1 and n=5. b) The energy released when electron translate from n =5 to n=1. c) the wavelength of the radiation emitted when electron translate from n= 5 to n= 1? 2. Find the quantum of energy of radiation emitted with a wavelength of 6.500 x 10 -10 m.
  • 13. 2. Find the energy of radiation when a mole of electron falls from energy level n =5 to energy level n = 2 in H atoms. Draw the energy levels diagram to show the translation of an electron involved.
  • 14.
    • Strong points of Bohr’s Theory :
    • Good in explaining the lines formation in H spectrum
    • Introduce the idea of quantum energy.
    Weaknesses of Bohr’s atomic Theory of H.
    • Able to explain the atomic spectrum of mono electron atom , like hydrogen or one-electron ions, such as He + or Li 2+ only. Unable to account the emission spectra of multi-electron atoms.
    • Could not explain extra lines appeared in the H emission spectrum when magnetic field is applied.
  • 15.
    • Development of Wave-particle duality of an electron:
    • Albert Einstein’s Photoelectric Effect Theory of light: Light has the properties of particle (photon) as well as wave.
    • Louis de Broglie suggested moving particles can exhibit wavelike properties. Hence electron can also has wave properties.
    3. Heisenberg Uncertainty Principle: It is impossible to know simultaneously the position and momentum of any moving particle.
  • 16.
    • Quantum or wave mechanics:( introduced by Erwin Schrodinger with its mathematical wave functions):
    • Solve the problems of finding/locating electrons .
    • The concept of electron density probability of finding an electron in a particular region of an atom. – high e density high probability of locating the e.
    • Concept of atomic orbital as region in space about the nucleus where there’s high probability ( 99 % ) of finding an electron.
  • 17. Concept of orbital
    • The different wave functions of electrons describe the different allowed shapes and energies of the electron waves .
    • Each of this diff possible waves, describing a region around the nucleus where the e is expected to be found = orbital.
    Examples of orbitals: S orbital One of the p orbitals How scientists describe fully an electron in an orbital of an atom?
  • 18. The four Quantum Numbers (QN)of an electron in an atom
    • An electron could be fully characterized by 4 quantum numbers:
    • Principal Quantum Number (n) principal energy level
    • The Azimuthal Quantum Number / Angular momentum quantum No ( l ) sub energy level ( orbital type)
    • The magnetic Quantum Number ( m l ) orientation of orbital
    • The electronic spin quantum number (m s ) spin of electron.
  • 19. 1. The Principal Quantum Number, n
    • n refer to the main energy level or electron shell of an electron
    • Integer value of n = 1, 2, 3,… 
    • relates to the average distance of an electron in a particular orbital from the nucleus of an atom.
    • larger the n value means higher E level, > average distance of electron from nucleus , > size of orbital, lesser is its stability.
    • n = 1 2 3 4
    • e - or quantum shell K L M N
  • 20. 2. The Azimuthal Quantum Number / Angular momentum quantum No., l
    • indicates the shape/type of the orbital sub energy levels / sub shells
    • For value of e shell n, it has n types of orbitals or subshell S ( ie. 3 values of L )
    • e.g. If n = 3 , we have 3 values of L , 3 sub shells
    • i.e. 3 s , 3 p , 3 d in quantum shell
    • /energy level n = 3
    What do we know from the value of quantum no. n and L ?
  • 21. value of l 0 1 2 3 4 Name of subshell s p d f g S =sharp, p = principal, d = diffuse, f= fundamental
    • Designation of orbitals of diff. l values :
  • 22. Sub shells of a quantum shell 5s, 5p,5d, 5f 5g 5 5 4s, 4p, 4d,4f 4 4 3s, 3p, 3d 3 3 2s, 2p 2 2 1s 1 1 Symbol No. of sub-shell Electron shell n
  • 23. Exercise: 1. State the no. of sub shells /sub energy levels for quantum shell n = 4. Name the sub shells. 2.i. How many orbital types/sub shells are there for n =1 ? Name it. ii. For energy level n = 4. State the no. of sub shells and name them. e.g. An electron with quantum no. n =3, how many subshells does it have? Name them. Ans: 3 subshells, I.e. 3s, 3p, 3d
  • 24. 3. The magnetic Quantum Number ( m L )
    • describes the orientation of the orbital in space
    • For a certain value of L , no. of integral values of m L = 2 L + 1 e.g. if L = 1 , it has = 2x 1 + 1 =3 values of m L = 3 orbitals of p x , p y , p z
    Quiz: For n =1, state the no. of values of I) L , ii) m L & .iii) the no. of subshells/orbital type, iv) no. of orbitals. i.e. No. of orbitals = 2 L + 1 for a certain value of L .
  • 25. What do we know from the value of quantum no. L and m L ? d x y d xz d yz d x 2 - y 2 d z 2 5 d P x , p y , p z 3 p s 1 s Symbol No. of orbitals Sub-shell
  • 26. 4.. The Electron spin quantum Number ( m s )
    • indicates the direction of spin of electron, clockwise or anticlockwise
    • Has only 2 values = + ½ , -½
    + ½ -½ Max. no. of e in 1 orbital = 2
  • 27.
    • For given quantum No. n , No. of subshell/sub energy level /orbital type = n
    • No. of orbitals = 2 L +1 (in a subshell L )
    • = no. of values of m L
    • = n 2 (in shell n )
    • 3. No. of electrons = 2 n 2 (in shell n )
    • = 2 (2 L +1 ) [in a subshell L ]
    • = 2 x no. of values of m L
  • 28. The shapes of atomic orbitals 1s 2s 3s z x y z z y y x x 2p x 2p y 2p z
  • 29. y x z y z z y x x z y x z x y d xy d xz d yz d x 2 - y 2 d z 2
  • 30.
    • Exercise:
    • 1.For energy level n = 2,
    • State the no. of : a) orbital types/subshells b) orbitals c) the max. no. of electrons.
    • Give the principal quantum no. of an electron in each of the following quantum shells : a) K quantum shell b) M quantum shell
    • For energy level n = 5, determine the no. of:
    • Values of l b) sub shell/sub energy levels c) orbitals
    • Maximum no. of electrons in a) each of the orbitals and b) each sub shells.
    • Maximum no. of electrons in quantum shell n = 5.
  • 31. Exercise 4. Sketch the shape of the the orbitals below: 1s, 2s, 3p x , 4p y , 5p z :, 3d xy , 3d x2-y2 Give one similarity and one difference between: a) 1s and 2s b) 3p x , 4p y , 5p z c) 3d xy ,, 3d x2-y2 5. For quantum shell n = 3, write the symbols of all the subshells in it. Hence the symbols of all the orbitals present.
  • 32. The relative energy levels of orbitals E n=4 n=3 n=2 n=1 1s 2s 2p (3 degerate orbitals) 3s 4s 3p (3 degerate orbitals) 3d (5 degerate orbitals) 4d (5 degerate orbitals) 4p (3 degerate orbitals) Order of energy levels: 1s < 2s < 2p < 3s < 3p < 4s < 3d
  • 33. Electronic configuration of the elements describes the arrangement of of electrons, by filling them in the orbitals, of a atom.
    • 2 ways of writing Electronic configuration:
    • e.g. The only electron of a ground state H atom is 1s 1 , or
    1s
    • 3 principles/rules for writing electronic configuration:
    • The Aufbau Principle (The Building up Principle)
    • The Pauli Exclusion Principle
    • Hund’s Rule
  • 34.
    • The Aufbau Principle (The Building up Principle)
    • Electrons are arranged in atomic orbitals in order of increasing energy. i.e. electrons should occupy lowest energy orbital 1 st before going into the next orbital with higher energy.
    • e.g. Z Element name elect config. 1 H 1s 1
    • 2 He 1s 2
    • 3 Li 1s 2 2s 1
    1s 2s 1s 1s
  • 35. The order of filling the atomic subshells ( orbitals) are in the foll. Sequence: 1s 2s 2p 3s 3p 3d 4s 4p 4d 4f 5s 5p 5d 5f 6s 6p 6d 7s 7p List the order of increase in energy of the above orbitals. 1s < 2s < 2p <3s < 3p < 4s < 3d < 4p < 5s < 4d < 5p < 6s
  • 36.
    • 2. The Pauli Exclusion Principle:
    • No 2 electrons in an atom can have the same 4 quantum numbers.
    • Electrons in any orbital must have the same values of n, l, ml but cannot have the same values of ms.
    • e.g. He atom of electronic configuration : 1s 2
    • Values of: I electron: n =1, l = 0, ml = 0, s = + ½ i.e. ( 1,0, 0, +½ )
    • Another electron n =1, l = 0, ml = 0, s = - ½ i.e. ( 1,0, 0, -½ )
    2s
  • 37. 3. Hund’s Rule: When electrons are added to orbitals of equivalent energy (degenerate orbitals), Each orbital is filled with a single electron of the same spin 1st before it is paired. e.g. The elect. Config. of 7 N 1s 2 2s 2 2p 3 1s 2s 2p x 2p y 2p z The elect. config of 8 O 1s 2 2s 2 2p 4 1s 2s 2p x 2p y 2p z Exercise: Write electronic conf. of F and Ne by continuing the process above using Hund’s Rule and Pauli Exclusion Principle..
  • 38. Writing electronic configuration of an element
    • General procedure: [e.g. e- conf. of Na]
    • Determine the no. of electrons i.e. No. of e - = Z (proton no.)
    • No. of e- of Na = 11 (i.e. Z)
    • 2. Apply Aufbau Principle : add e - to subshells/ orbitals in order of increasing energy
    • 3. Use Pauli Exclusion Principle: i.e. One orbital can only has 2 e- and their spins must be opposite
    • 4. Follow Hund’s Rule: Each orbital is filled with a single electron of the same spin 1st before it is paired.
    1s 2s 2p x 2p y 2p z 3s 1s 2 2s 2 2p 6 3s 1 Valence e. config. 3s 1
  • 39. e.g. Write electronic configuration of I. 26 Fe ii. 26 Fe 2+ iii. 24 Cr 3+ ANS: i. 26 Fe : 1s 2 2s 2 2p 6 3s 2 3p 6 4s 2 3d 6 Remember and use orbitals’ E level in ascending order list : 1s < 2s < 2p <3s < 3p < 4s < 3d < 4p < 5s < 4d < 5p < 6s ii. Rearrange i . to be 1s 2 2s 2 2p 6 3s 2 3p 6 3d 6 4s 2 Then 26 Fe 2+ e - config . : 1s 2 2s 2 2p 6 3s 2 3p 6 3d 6 4s 0
    • 24 Cr : 1s 2 2s 2 2p 6 3s 2 3p 6 3d 5 4s 1
    • 24 Cr 3+ 1s 2 2s 2 2p 6 3s 2 3p 6 3d 3 4s 0
    - 3e - 2e
  • 40. Exercise: 1. Write the electronic configuration of the following species by using: I. the s, p, d,f notation ii. An orbital diagram.: a) Cl (Z= 17) d) Zn 2+ (Z = 30) b) K + ( Z = 19) e) Mn 4+ (Z =24) c) S 2- ( Z = 16) d) Cu + (Z = 29) 2. Write the electronic configuration in orbital notation of : a) Na b) N c) B d) Se Underline the electronic configuration of their respective valence shells.
  • 41. Anomalous E. conf. – exception to the Aufbau Principle In terms of orbital diagram: Cr [Ar] 3d 4s Reason: a half –filled 3d subshell has extra added stability. In terms of orbital diagram: Cu [Ar] 3d 4s Reason: a filled 3d subshell has extra added stability. [Ar]3d 5 4s 1 [Ar]3d 10 4s 1 [Ar]3d 4 4s 2 [Ar]3d 9 4s 2 Cr (Z =24) Cu( z = 29) Observed Expected Element
  • 42. Short revision quiz
    • State the formula used to calculate energy of electron at energy level n = 2
    • Give the equations (formulae) used for the following computations where relevant: a. If an electron is excited to quantum shell n = 3 from its ground state, n =1 what is the energy required?
    • b. What is the frequency of the light energy absorbed?
    • c. Determine its wavelength?
    • 3. Draw the energy diagram for the translation of electron from energy level n =2 to n = 5 in a mole of H atoms.
  • 43.
    • 4. Arrange the orbital type/ electron subshell in order of ascending energy :
    • 1s 2s 2p 3s 5p 3p 3d 4s 4p 4d 5s 6s
    • How many electrons can be filled into each orbital?
    • b. State the maximum no. of electrons allowed in each e - subshell.
    6. Write orbital diagram for P. State the total no. of paired electrons and unpaired electrons in it. 7. Write electronic and orbital diagram for Ti (Z= 22). Name the 2 Principles and one rule used. 8. How many electrons in: i.. 2p subshell, ii 3d orbitals, iii. 4s orbital and iv. Quantum shell n = 4 ?
  • 44. Formulae to remember and apply 1.Energy of electron at energy level n, E n = - A / n 2 (Bohr equation) 2. Amount of energy released or absorbed by electron(photon) :  E = E f – E i = A( 1/n i 2 – 1/n f 2 ) 3. Planck relate energy of a radiation to its frequency or wavelength : E = h  or E = h c/ 
  • 45.
    • For given quantum No. n , No. of subshell/sub energy level /orbital type = n
    • No. of orbitals = 2 L +1 (for subshell L )
    • = no. of values of m L = n 2 (for shell n )
    • 3. No. of electrons = 2 n 2 (for shell n )
    • = 2 (2 L +1 ) [for subshell L ]
    • = 2 x no. of values of m L

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