This is a follow up on the two previous posts letting RealQM explain the weak reactivity of Gold Au as compared to the strong reactivity of Caesium Cs both in 6th row of the periodic table having one valence electron. The same argument applies to Silver Ag vs Rubidium Rb (5th row) and Copper Cu vs Potassium K (4th row).
Recall the following electron configurations (number of electrons in expanding sequence of shells)
- Au: 2+8+18+32+18+1 79 electrons in 6 shells
- Cs: 2+8+18+18+8+1 55 electrons in 6 shells
- Ag: 2+8+18+18+1 47 electrons in 5 shells
- Rb: 2+8+18+8+1 37 electrons in 5 shells
- Cu: 2+8+18+1 29 electrons in 4 shells
- K: 2+8+8+1 19 electrons in 4 shells
We observe that the electron sequences for Au, Ag and Cu end with 18+1, while Cs, Rb and K end with 8+1.
We compute using RealQM in a spherical symmetric form to get the following radius R in atomic units of the outermost shell containing the valence electron
We observe that the radius for Au is smaller than that of Cs although Au contains 22 more electrons than Ce. The same pattern for Ag vs Rb and Cu vs K.
In the previous post we gave explanations using RealQM along the following lines of thought:
- Weaker reactivity by more tightly bound valence electron for smaller radius in same row moving right.
- Reactivity weakens as radius increases down the column of Cu, Ag and Au because binding by electron sharing is increasingly counteracted.
RealQM thus allows an explanation of the weak reactivity of Gold based on the Atomic model of RealQM as an a new form of Schrödinger equation based on non-overlapping one-electron charge densities/wave functions.
To understand it is necessary to keep two ideas in mind at the same time when inspecting the Periodic Table as an elaboration of 1. and 2. above:
- Reactivity increases moving left in a row because of increasing inner shell radius (8+1 instead of 18+1).
- Reactivity decreases moving down a column because of increasing inner shell radius (more electrons).
Here 1. expresses that moving left in a row decreases the attraction from the inner shells coming with increased reactivity.
Here 2. as an the effect of increasing inner shell radius can be illustrated as follows:
 |
| Small radius of inner shells (red): Binding (green) |
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| Large radius of inner shells (red): Small binding (green). |
Recall that StandardQM offers an explanation based on an idea that a Gold atom has inner electrons reaching half the speed of light with increased mass binding the valence electron. It is a mind-boggling explanation. More precisely, the value of relativity theory is that it can explain any observation outside mainstream science as a relativistic effect. That the relativistic effect is very strong for Au(79) but very weak for Cs (55) is hard to accept, since they can differ by at most a factor $(55/79)^2\approx 0.5$.
Here are the basic (3) lines of the code: update of electrons, potential and free boundary:
//Update of shell-electron wave functions
for (var q=1;q<Q+1;q++){
for (var i=M[q-1]+1;i<M[q]-1;i++){
u[i]=u[i]+0.5*dt*(u[i+1]-2*u[i]+u[i-1])/pow(h,2)+0.5*dt*(u[i+1]-u[i-1])/(h*i*h) + dt*K[i]*u[i] - dt*2*P[i]*u[i];
}
//Normalisation of shell-electron charge
normu[q]=0;
for (var i=M[q-1];i<M[q];i++){
normu[q]= normu[q] + pow(u[i]*(i*h),2)*h;
}
for (var i=M[q-1];i<M[q];i++){
u[i]=sqrt(E[q])*u[i]/sqrt(normu[q]);
}
//Update of shell-electron potentials
for (var q=0;q<Q+1;q++){
for (var i=M[q]+1;i<M[q+1]+1;i++){
P[i]=0;
for (var j=1;j<N+1;j++){
P[i]=P[i]+0.5*pow(u[j],2)*pow(j*h,2)*h*min(1/(i*h),1/(j*h));
if (j>M[q] && j<M[q+1]){
P[i]=P[i]-0.25*pow(u[j],2)*pow(j*h,2)*h*min(1/(i*h),1/(j*h));
}
}
}
}
//Update of free boundary
for (var q=Q0+1;q<Q;q++){
if (u[M[q]]>u[M[q]-1]+diff){
M[q]=M[q]-2;
}
if (u[M[q]]<u[M[q]-1]-diff){
M[q]=M[q]+1;
}
}
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