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 ).

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:

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:

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.

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

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

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

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

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

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..

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

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/ 