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.

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 n^th orbit of a hydrogen- like atom is given as E_n = -(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°