Top page (correct Bohr model including helium).
Back to hydrogen molecule page.
If you copy and paste the program source code below into a text editor, you can easily compile and run this.
(This class file name is hymol, so save this text editor as "hymol.java", and compile it.)
Here we use the new unit of 1 MM = 1 × 10-14 meter.
In this program, first we input the internuclear distance (in MM ) of H2.
And then input y-coordinate "r" (in MM) , and x-coordinate "a" ( in MM ) of electron 1.
From the inputted values, this program outputs the binding energy (eV) of H2, total force acting on nucleus 1 (nucforce), x,y components of forces acting on electron 1 (= elefx, elefy ).
These forces are expressed as the ratio to the force between electron and nucleus of H atom's ground state.
From the force acting on electron and its velocity, we calculate the number of de Broglie wave in one orbit.
( Here Virial theorem E = -T = 1/2 V is used. )
"another x" means another x coordinate of electron 1 moving in the direction of force.
The initial x-coodinate is automatically increased per calculation until +100.
import java.util.Scanner;
class hymol {
public static void main(String[] args) {
Scanner stdIn=new Scanner(System.in);
System.out.println(" Internuclear distance (MM) of H2 molecule ? ");
double nnuc=stdIn.nextDouble();
System.out.println(" r (MM)？ = y coodinate of electron 1 ");
double rr=stdIn.nextDouble();
System.out.println(" a (MM) ? = x coodinate of electron 1 ");
double aa=stdIn.nextDouble();
double me=9.1093826e-31;
double pai=3.141592653589793; double epsi=8.85418781787346e-12;
double h=6.62606896e-34; double ele=1.60217653e-19;
double boh=5292.0*5292.0*1.0e-28; // boh = ( Bohr radius )^2
double r=rr*1.0e-14;double nuc=nnuc*1.0e-14; // change MM to meter
double ke=(ele*ele)/(4.0*pai*epsi);
for (int i=1;i < 10;i++){ // repeat calculation from a to a + 10*10 (MM)
double a=aa*1.0e-14;
double rra=Math.sqrt(a*a+r*r); // rra =distance between electron 1 and n1
double rrb=Math.sqrt(r*r+(nuc-a)*(nuc-a)); // rrb= between electron 1 and n2
double rrc=Math.sqrt(4*r*r+(nuc-2*a)*(nuc-2*a)); // between two electrons
double poten=ke*(-2.0/rra-2.0/rrb+1.0/nuc+1.0/rrc); // poten=potential energy (J)
double ppot=poten*6.241509*1.0e18; // ppot = potential energy (eV)
double kinetic=-0.5*poten; // kinetic = total kinetic energy of two electrons (J)
double velo=Math.sqrt(kinetic/me); // velo = electron's velocity (m/s)
double binding=-ppot*0.5-13.606*2; // binding energy (eV) of H2
// foeces acting on electron 1 ( x, -y directions )
double elefx= -a/(rra*rra*rra) + (nuc-a)/(rrb*rrb*rrb) - (nuc-2*a)/(rrc*rrc*rrc);
double elefy= r/(rra*rra*rra) + r/(rrb*rrb*rrb) - (2*r)/(rrc*rrc*rrc);
double eleforce = ke*Math.sqrt(elefx*elefx + elefy*elefy); // total force
double radius=(me*velo*velo)/eleforce; // rotation radius from centrifugal force
double debroglie = h/(me*velo); // de Broglie wavelength of electron
double wave=(2*pai*radius)/debroglie; // wave's number in one orbit
double nucforce= a/(rra*rra*rra)-1.0/(nuc*nuc)+(nuc-a)/(rrb*rrb*rrb);
nucforce=nucforce * boh; // total force acting on nucleus 1
double anotherx=a+(2.0*r*elefx)/elefy;
anotherx = anotherx * 1.0e14; // another x coordinate of electron 1
elefx=elefx * boh; elefy = elefy * boh;
System.out.printf("a:%.1f ", aa);
System.out.printf(" binding-energy: %.4f ", binding);
System.out.printf(" elefx: %.3f ", elefx);
System.out.printf(" elefy: %.3f \n", elefy);
System.out.printf("nucforce: %.3f ", nucforce);
System.out.printf(" another x : %.2f ", anotherx);
System.out.printf(" de Broglie wave: %.3f \n", wave);
System.out.printf(" \n");
aa=aa+10;}}}