Consider a two-electron atom in which the electrons, orbiting a nucleus of charg
ID: 1915409 • Letter: C
Question
Consider a two-electron atom in which the electrons, orbiting a nucleus of charge +Ze, follow Bohr-like orbits of the same radius r, with the electrons always on opposite sides of the nucleus.
a) Show that the new force on each electron is toward the nucleus and has magnitude:
F=(e^2)/(4 pi epsilon r^2) (Z-1/4)
b) Use the fact that this is the centripetal force to show that the square of each electrons orbital speed v is given by:
v^2=(e^2)/(4 pi epsilon m*r) (Z-1/4)
c) Use the resulf of part b along with Bohr's rule that the angular momentum of each of the two electrons is L=h-bar in the ground state to show that:
r= (epsilon*h^2)/(pi*m*e^2(Z-1/4))
d) Show that the atom's total energy (kinetic plus potential) is:
E= -((m*e^4)/(8*epsilon^2*h^2))(2Z-1/2)(Z-1/4)
e)The energy needed to remove both electrons is just the neative of the energy you found in part d. compute the energy needed to remove obother electrons in helium, and then repeat for Li+. Compare your reslt witht the experimental values of 79.0 eV and 198 eV respectively.
Explanation / Answer
f1=Ze*e/4r^2 it is force between electron and nucleus
f2=e*e/4*4r^2 it is between two electrons
a)total resultant=f1-f2 =(e^2/4r^2)*(z-1/4)
b)centripetal force=mv^2/r=(e^2/4r^2)*(z-1/4)
that gives v^2=(e^2/4r*m)*(z-1/4)