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 Li^{2+} form the first to the third Bohr orbit. Given the

ionization energy of hydrogen atom as 13.6 eV.

Sol: The energy of n^{th} orbit of a hydrogen- like atom is given as E_{n} = -(13.6 Z^{2})/n^{2} Thus for Li^{2+} from, as Z = 3,

The electron energies of the first and third Bohr orbits are for n = 1, E_{1} =-122.4 eV, for

n = 3, E_{3} = -13.6 eV.

Thus the energy required to transfer an electron from E_{1} level to E_{3} level is,

E= E_{3}– E_{1} = -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°