The Modern Picture of an Atom 0.11 0.18 ● 0.32 0.05 The best we can do is say what the probability of finding an electron is at any given point for any individual observation Such information is described by a function with properties of a wave,hence the name WAVEFUNCTION Π-6
The Modern Picture of an Atom The best we can do is say what the probability of finding an electron is at any given point for any individual observation Such information is described by a function with properties of a wave, hence the name WAVEFUNCTION 0.11 0.18 0.32 0.05 II-6
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II-7
Waves in 1-D 0 d For this example, But f also varies with time y=f(x)=A sin X d y f(x,t)=A sin d cos(ωt) The function is called the Wavefunction: 平xt) Π-8
Waves in 1–D A d For this example, But f also varies with time The function is called the Wavefunction: Ψ(x,t) 0 y= f(x) = A sin ( πx d ) y = f(x,t) = A sin cos (ωt) ( πx d ) II-8
Boundary Conditions to Define Allowed Waves: 1)Tie the Ends Down 2)Find a Standing Wave in the Box Allowed Standing Wave Ends are fixed at =0 always Not an Allowed Wave Not Even a Standing Wave Ends not Tied Down A Traveling Wave L-9
Allowed Standing Wave Ends are fixed at Ψ = 0 always Not an Allowed Wave Ends not Tied Down Not Even a Standing Wave Boundary Conditions to Define Allowed Waves: 1) Tie the Ends Down 2) Find a Standing Wave in the Box A Traveling Wave II-9
Nodes ThisΨhas No Nodes There are no points for which=0 at all times (The ends were fixed by the boundary conditions and therefore don't count as nodes) L-10
Nodes There are no points for which Ψ = 0 at all times (The ends were fixed by the boundary conditions and therefore don’t count as nodes) This Ψ has No Nodes II-10