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
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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.
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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.
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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 ).
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
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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
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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:
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.
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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:
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
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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:
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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.
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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.
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.
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.
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
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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 ?
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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 :
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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
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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
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 .
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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
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.
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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.
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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
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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:
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
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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
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
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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..
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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
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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
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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.
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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
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.
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 ?
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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/