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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 Hyatom, so save this text editor as "Hyatom.java", and compile it.)
In this program, we first input the initial x-coordinate r1 (in MM) of electron 1 and the absolute value of the total energy E ( in eV ) of the hydrogen atom 1S orbit.
Here we use the new units, ( 1 MM = 10-14 meter, 1 SS = 10-22 second, 1 MM/SS = 108 m/s ).
From the inputted values, this program outputs the last velocity ( VX,VY in MM/SS ) and number of the de Broglie's waves ( midWN ) contained in one quarter of the orbit.
import java.util.Scanner;
class Hyatom {
public static void main(String[] args) {
Scanner stdIn=new Scanner(System.in); // input r1 and |E|
System.out.println("r1 between nucleus and electron 1 (MM) ?");
double r=stdIn.nextDouble();
System.out.println("total energy |E| in the 1S hydrogen atom (eV) ? ");
double E=stdIn.nextDouble();
double me=9.1093826e-31; double mp=1.67262171e-27;
double rm=(me*mp)/(me+mp); // rm = reduced mass of electron in H atom
double pai=3.141592653589793; double epsi=8.85418781787346e-12;
double h=6.62606889e-34; double ele=1.60217653e-19;
// Bor = theoretical value of Bohr radius (MM) (of reduced mass)
// Ene = theoretical value of total energy |E| (eV) in 1S hydrogen
double Bor=(epsi*h*h*1.0e14)/(pai*ele*ele*rm);
double Ene=(ele*ele*ele*ele*rm*6.241509e18)/(8.0*epsi*epsi*h*h);
double Exe=13.59844; // Exe = experimental value of ionization energy (eV) of H atom.
System.out.printf("theoretical value of Bohr radius (MM):%.5f \n ", Bor);
System.out.printf("theoretical value of |E| (eV) in H atom :%.5f \n ", Ene);
System.out.printf("experimental value of ionization energy (eV) in H atom :%.5f \n ", Exe);
for (int i=1;i < 30;i++) { // repeat until r1=initial r1+30
// calculation of initial VY from E and r1
double poten=-(ele*ele)/(4.0*pai*epsi*r);
//vya (J) = total E-potential energy
double vya=-(E*1.60217646e-19)-poten*1.0e14;
if (vya > 0) {
// vyb=velocity from kinetic energy
double vyb=Math.sqrt((2.0*vya)/rm);
double VY=vyb*1.0e-8; // change m/sec to MM/SS
double prexx=r; double VX=0.0; double WN=0.0; double preyy=0.0;
double xx,yy,vk,preVY,preWN,midWN;
do {
xx=prexx+VX; yy=preyy+VY; //electron 1 position after 1SS
preVY=VY;preWN=WN ;
vk=VX*VX+VY*VY; //calculation of WN from VX,VY
// WN=WN+ number of de Broglie wave contained in short segment
WN=WN+(rm*vk*1.0e-6)/h;
//calculation of VX,VY from Coulomb force
double ra=Math.sqrt(prexx*prexx+preyy*preyy);
ra=ra*1.0e-14; // change MM to meter
prexx=prexx*1.0e-14; preyy=preyy*1.0e-14;
double ac=(ele*ele)/(4.0*pai*epsi*rm);
// change velocity components VX (MM/SS) and VY from Coulomb force
VX=VX+1.0e-30*ac*prexx*(-1.0/(ra*ra*ra));
VY=VY+1.0e-30*ac*preyy*(-1.0/(ra*ra*ra));
prexx=xx;preyy=yy;
} while (xx > 0); //repeat above until electron 1 arive at y axis
if (VY > -0.0001 && VY < 0.0001) { // last VY condition
System.out.print("r1: "+r+" ");
System.out.printf("VX:%.5f ", VX);
System.out.printf("VY:%.5f ", VY);
System.out.printf("preVY:%.5f ", preVY);
midWN=(WN+preWN)/2.0; System.out.printf("midWN:%.5f \n", midWN);
}
} r=r+1;
}}}