Consider the ground state Li+ ion (Z=3) in terms of the Bohr’s model: two 1s electrons in the lowest allowed circular orbit around the nucleus.
a)Calculate the ion total energy (in eV) neglecting the electron-electron repulsion
Electron 1 sees a net charge of +2e in the nucleus, so Z=3 and n=1
E = -13.6 ev * (3)/1
E = -122.4 ev
Neglecting electron- electron interaction, the Ion total energy of the electrons in the Li+ atom is:
EIon-totall = -122.4 ev ...Is this correct?
b)Calculate the electron-repulsion (Coulomb) energy and add it to the value obtained in (a)
a= a0/Z , a = 5.29 x 10-11 m/3 =1.7633 x 10-11
έ0 = 8.854 x 10-12 F/M, e= 1.602 x 10-19 C , q= 1.602 x 10-19 J/ev
P.E = 40.8 ev
Ee-e =40.8
Is this correct?
c) Determine the exact energy of the ion in terms of experimental ionization energies IE
d) Predict the electron-repulsion energy from the experimental IE values
e)Using the experimental IE values, calculate Zeff for the two electrons in Li+.