Unformatted text preview: Quantum or Wave Mechanics
de Broglie (1924) proposed de Broglie (1924) proposed that all moving objects that all moving objects have wave properties. have wave properties. For light: E = mc 22 For light: E = mc E = hν = hc // λ E = hν = hc λ hc
L. de Broglie (18921987) Quantum or Wave Mechanics
Baseball (115 g) at 100 mph λ = 1.3 x 10 32 cm 1.3 cm e with velocity = 1.9 x 108 cm/sec cm/sec λ = 0.388 nm 0.388 Quantum or Wave Mechanics
Schrodinger applied idea of ebehaving as a wave to the problem of electrons in atoms. He developed the WAVE WAVE EQUATION
Solution gives set of math expressions called WAVE E. Schrodinger FUNCTIONS, Ψ
18871961 Therefore, mc = h // λ Therefore, mc = h λ and for particles and for particles (mass)(velocity) = h // λ (mass)(velocity) = h λ Experimental proof of wave properties of electrons Each describes an allowed energy state of an eQuantization introduced naturally. WAVE FUNCTIONS, Ψ
• Ψ is a function of distance and two is
angles. • Each Ψ corresponds to an ORBITAL corresponds ORBITAL — the region of space within which an electron is found. Uncertainty Principle
Problem of defining nature Problem of defining nature of electrons in atoms of electrons in atoms solved by W. Heisenberg. solved by W. Heisenberg. Heisenberg. Cannot simultaneously Cannot simultaneously define the position and define the position and momentum (= m•v) of an momentum (= m•v) of an electron. electron. We define e energy exactly We define e energy exactly but accept limitation that but accept limitation that we do not know exact we do not know exact position. position. Types of Orbitals
s orbital p orbital d orbital • Ψ does NOT describe the exact does
location of the electron. W. Heisenberg 19011976 • Ψ2 is proportional to the probability of is
finding an e at a given point. Page 1 Orbitals
• No more than 2 e assigned to an orbital • Orbitals grouped in s, p, d (and f) subshells
No. orbs. No. es orbitals d orbitals p orbitals Subshells & Shells
• Subshells grouped in shells. • Each shell has a number called the PRINCIPAL QUANTUM NUMBER, n • The principal quantum number of the shell is the number of the period or row of the periodic table where that shell begins. s orbitals s orbitals d orbitals p orbitals p orbitals d orbitals 1 2 3 6 5 10 Subshells & Shells
n=1 n=2 n=3 n=4 QUANTUM NUMBERS
Each orbital is a function of 3 quantum numbers: Symbol n (major) shell subshell designates an orbital within a subshell QUANTUM NUMBERS Values 1, 2, 3, .. Description n (major) > (major) > l (angular) > (angular) > ml (magnetic) > (magnetic) > Orbital size and energy where E = R(1/n 2) l (angular) 0, 1, 2, .. n1 Orbital shape or type (subshell) subshell) ml (magnetic) l..0..+l Orbital (magnetic) orientation # of orbitals in subshell = 2 l + 1 Page 2 Shells and Subshells Shells and Subshells
When n = 1, then l = 0 and m l = 0 Therefore, in n = 1, there is 1 type of subshell and that subshell has a single orbital (ml has a single value > 1 orbital) has This subshell is labeled s (“ess”) (“ess”) Each shell has 1 orbital labeled s, and it is SPHERICAL in shape. SPHERICAL in s Orbitals s Orbitals
All s orbitals are spherical in shape . 1s Orbital See Figure 7.14 on page 319 and See Figure 7.14 on page 319 and Screens 7.10 and 7.11. Screens 7.10 and 7.11. 2s Orbital 3s Orbital p Orbitals Typical p orbital Typical p orbital When n = 2, then ll = 0 and 1 When n = 2, then = 0 and 1 Therefore, in n = 2 shell Therefore, in n = 2 shell there are 2 types of there are 2 types of planar node orbitals — 2 subshells planar node orbitals — 2 subshells For ll = 0 mll = 0 For = 0 m = 0 When l = 1, there is this is a s subshell tthis is a s subshell a his PLANAR NODE For ll = 1 m ll = 1, 0, +1 For = 1 m = 1, 0, +1 1, thru this is a p subshell this is a p subshell the nucleus. with 3 orbitals with 3 orbitals with See Screens 7.11 and 7.13 Page 3 p Orbitals p Orbitals
pz 2px Orbital Orbital 2py Orbital Orbital 90o px py A p orbital The three p orbitals lie 90o apart in space 2pz Orbital Orbital 3px Orbital Orbital 3py Orbital Orbital Page 4 3pz Orbital Orbital
l = 0, 1, 2 d Orbitals d Orbitals
When n = 3, what are the values of l? and so there are 3 subshells in the shell. For l = 0, ml = 0 > s subshell with single orbital > For l = 1, ml = 1, 0, +1 1, > p subshell with 3 orbitals For l = 2, ml = 2, 1, 0, +1, +2 2, > d Orbitals d Orbitals typical d orbital planar node d subshell with 5 orbitals s orbitals have no planar node (l = 0) and so are spherical. p orbitals have l = 1, and have 1 planar node, and so are “dumbbell” shaped. This means d orbitals (with l = 2) have 2 planar nodes planar node See Figure 7.16 See Figure 7.16 3dxy Orbital Orbital 3dxz Orbital Orbital 3dyz Orbital Orbital Page 5 3dz2 Orbital Orbital 3dx2 y2 Orbital Orbital f Orbitals f Orbitals
When n = 4, l = 0, 1, 2, 3 so there are 4 subshells in the shell. For l = 0, ml = 0 > s subshell with single orbital > For l = 1, ml = 1, 0, +1 1, > p subshell with 3 orbitals For l = 2, ml = 2, 1, 0, +1, +2 2, > d subshell with 5 orbitals For l = 3, m l = 3, 2, 1, 0, +1, +2, +3 3, > f subshell with 7 orbitals Shell Principal Quantum Number, n 1 2 3 Relate to n No. Subshells No. Orbitals No. e 1 1 2 2 4 8 3 9 18 =n = n2 = 2 n2 Page 6 ...
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This note was uploaded on 01/11/2011 for the course ENGINEERIN MAE 107 taught by Professor Pozikrizdis during the Fall '08 term at San Diego.
 Fall '08
 POZIKRIZDIS

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