Q: A doubly ionized lithium atom is hydrogen like with atomic number Z = 3. Find the wavelength of the
radiation required to excite the electron in Li2+ form the first to the third Bohr orbit. Given the
ionization energy of hydrogen atom as 13.6 eV.
Sol: The energy of nth orbit of a hydrogen- like atom is given as En = -(13.6 Z2)/n2 Thus for Li2+ from, as Z = 3,
The electron energies of the first and third Bohr orbits are for n = 1, E1 =-122.4 eV, for
n = 3, E3 = -13.6 eV.
Thus the energy required to transfer an electron from E1 level to E3 level is,
E= E3– E1 = -13.6-(-122.4) = 108.8 eV.
Therefore, the radiation needed to causes this transition should have photons of this energy. hv = 108.8 eV.
The wavelength of this radiation is , λ = hc/(108.8 eV)= 114.25 A°