Weak Reactivity of Gold Explained by RealQM

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 

• Au: R = 2.94  (run code by pressing start)
• Cs: R = 3.36   (code)
• Ag: R = 2.45  (code)
• Rb: R= 2.85    (code)           

We observe that the radius for Au is somewhat 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:

1. Weaker reactivity by more tightly bound valence electron for 18+1 than 8+1.
2. Weaker reactivity down the column of Cu, Ag and Au because binding by electron sharing is increasingly counteracted.    

Here 1. expresses common insight, while 2. is new insight brought by RealQM, which can be illustrated as follows:

Small radius of inner shells (red): Binding (green)

  

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 is an illuminating chat with GPT. In particular the seemingly contradictory fact that Francium Fr (87) has stronger relativistic effect and stronger reactivity is discussed.

Here are the basic (3) lines of the RealQM 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];

 if (q<Q}

  u[M[q]]=u[M[q]+1];

  u[M[q]-1]=u[M[q]-2];

}

}

//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=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;

  }

}