CHAPTER 8

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CHAPTER 8THE helium ATOMThe second element in the periodic table provides our rst example of aquantum-mechanical problem whichcannotbe solved exactly. Nevertheless,as we will show, approximation methods applied to helium can give accuratesolutions in perfect agreement with experimental results. In this sense,it can be concluded that quantum mechanics is correct for atoms morecomplicated than hydrogen. By contrast, the Bohr theory failed miserablyin attemps to apply it beyond the hydrogen helium atom has two electrons bound to a nucleus with chargeZ= 2. The successive removal of the two electrons can be diagrammed asHeI1 !He++e I2 !He+++ 2e (1)The rst ionization energyI1, the minimum energy required to remove the rst electron from helium , is experimentally eV. The second ionizationenergy,I2, is eV. The last result can be calculated exactly since He+is a hydrogenlike ion. We haveI2= E1s(He+) =Z22n2= 2 hartrees = 54:42 eV(2)The energy of the three separated particles on the right side of Eq (1) is, byde nition, zero.

CHAPTER 8 THE HELIUM ATOM The second element in the periodic table provides our flrst example of a quantum-mechanicalproblem whichcannotbesolved exactly.

  Chapter, Chapter 8, Helium