At_Struct_2

At_Struct_2 - Quantum or Wave Mechanics Quantum or Wave...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Quantum or Wave Mechanics 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 L. de Broglie (1892-1987) Therefore, mc = h // λ Therefore, mc = h λ and for particles and for particles Experimental proof of wave properties of electrons angles. — the region of space within which an electron is found. location of the electron. EQUATION e- with velocity = 1.9 x 108 cm/sec Solution gives set of math expressions called WAVE expressions WAVE E. Schrodinger FUNCTIONS, Ψ FUNCTIONS, 1887-1961 λ = 0.388 nm Each describes an allowed energy state of an eQuantization introduced naturally. Uncertainty Principle • Each Ψ corresponds to an ORBITAL Each ORBITAL • Ψ2 is proportional to the probability of He developed the WAVE He WAVE λ = 1.3 x 10 -32 cm • Ψ is a function of distance and two is • Ψ does NOT describe the exact Schrodinger applied idea of ebehaving as a wave to the problem of electrons in atoms. Baseball (115 g) at 100 mph ((mass)(velocity) = h // λ mass)(velocity) = h λ WAVE FUNCTIONS, Ψ WAVE Quantum or Wave Mechanics W. Heisenberg 1901-1976 Problem of defining nature Problem of defining nature of electrons in atoms of electrons in atoms solved by W. Heisenberg . solved by W. 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. finding an e- at a given point. Types of Orbitals s orbital p orbital d orbital Page 1 Orbitals • No more than 2 e- assigned to an orbital • Orbitals grouped in s, p, d (and f) subshells s orbitals d orbitals s orbitals s orbitals p orbitals d orbitals Subshells & Shells n=1 n=2 n=3 n=4 Subshells & Shells p orbitals p orbitals d orbitals No. orbs. 1 3 5 No. e- 2 6 10 • Subshells grouped in shells. • Each shell has a number called the PRINCIPAL QUANTUM PRINCIPAL 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. QUANTUM NUMBERS Each orbital is a function of 3 quantum numbers: n (major) ---> (major) ---> l (angular) ---> ml (magnetic) ---> (magnetic) shell subshell subshell designates an orbital within a subshell within Page 2 QUANTUM NUMBERS Symbol Values n (major) 1, 2, 3, .. Description Orbital size and energy where E = -R(1/n 2) l (angular) 0, 1, 2, .. n-1 Orbital shape or type or (subshell) ml (magnetic) -l..0..+l Orbital Orbital orientation orientation # of orbitals in subshell = 2 l + 1 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) s Orbitals s Orbitals 1s Orbital All s orbitals are spherical in shape . This subshell is labeled s (“ess”) Each shell has 1 orbital labeled s, and it is SPHERICAL in shape. and SPHERICAL in 2s 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. 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 tthis is a s subshell his is a s subshell a PLANAR NODE For ll = 1 m ll = --1, 0, +1 For = 1 m = 1, 0, +1 thru tthis is a p subshell his is a p subshell the nucleus. with 3 orbitals with 3 orbitals See Screens 7.11 and 7.13 Page 3 2px Orbital p Orbitals p Orbitals 2py Orbital 3px Orbital 3py Orbital pz 90o A p orbital px py The three p orbitals lie 90o apart in space 2pz Orbital Page 4 d Orbitals d Orbitals 3pz Orbital When n = 3, what are the values of l? l = 0, 1, 2 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 ---> p subshell with 3 orbitals ---> For l = 2, ml = -2, -1, 0, +1, +2 ---> 3dxy Orbital d subshell with 5 orbitals 3dxz Orbital Page 5 d Orbitals d Orbitals typical d orbital 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 planar node See Figure 7.16 See Figure 7.16 3dyz Orbital 3dz2 Orbital 3dx2- y2 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 ---> p subshell with 3 orbitals ---> For l = 2, ml = -2, -1, 0, +1, +2 ---> d subshell with 5 orbitals ---> For l = 3, m l = -3, -2, -1, 0, +1, +2, +3 ---> f subshell with 7 orbitals ---> Shell Principal Quantum Number, n 1 2 3 Relate to n No. Subshells No. Orbitals 1 2 3 =n 1 4 9 = n2 No. e- 2 8 18 = 2 n2 Page 6 ...
View Full Document

Ask a homework question - tutors are online