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set2 - Thewavefunc,on(x...

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The wave func,on ψ(x) Interpreta,on and condi,ons Ψ * (x)Ψ(x)dx=P(x)dx the probability of finding the system between x and x+dx Probability (density) must always be posi,ve Ψ * (x)Ψ(x) > 0 Note that the wave func,on itself need not be posi,ve. In fact it is a complex func,on ψ x ( ) = a x ( ) + ib x ( ) = A x ( ) exp i μ x ( ) ( ) i = 1
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Bohr model of atoms The electron are moving in exact circles around the nucleus The electron centrifugal energy is pushing it away. Electrosta,c aJrac,on brings it in.
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The Bohr model (one electron system) Basic assump,ons: 1. To keep the electron in circular orbit the radial forces must cancel Radial force: Electrosta,c force: (atom with one electron but nucleus charge Ze) 2. Electrons that are at a sta,onary state do not radiate and have angular momentum mv 2 r Ze 2 r 2 J = mvr = n n = 1,2,3,... = h 2 π h : Planck constant
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Radius of single‐electron atoms from Bohr’s model 1. force comparison 2. Angular momentum condi,on 3. Subs,tu,ng (1) in (2) mv 2 r = Ze 2 r 2 mvr = n v = n mr m n mr 2 r = Ze 2 r n 2 2 mr 2 = Ze 2 r r = n 2 2 Zme 2 a 0 = 2 me 2 (Bohr radius)
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Ioniza,on energy (I) When the distance between the nucelus and the electron is very large, the electron is dissociated from the proton(s), and the interac,on energy between the electron and the proton(s) must be zero p e E = 1 2 mv 2 Ze 2 r using the centrifugal/electrostatic force relation mv 2 r = Ze 2 r 2 mv 2 = Ze 2 r E = Ze 2 2 r r →∞ 0
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Ioniza,on energy (II)
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