(a)Find the wavelength of the radiation required to excited the electron is `Li^(++)` from the first to the third Bohr orbit (b) How many spectral lines are obseved in the emission spactrum of the above excited system?

Explanation

(a) The energy in the first orbit `= E_(1)= Z^(2)E_(0)where E_(0) = -13.6eV` is the energy of a hydrogen atom in ground state Thus for`Li^(++)`
`E_(1) = 9E_(0)= 8 xx (113.6eV)`
The energy in the third orbit is
`E_(0) = (E_91))/(n^(1)) = (E_(1))/(9) = - 13.6eV`
`Thus, E_(0) - E_(1) = 8 xx 13.6eV = 108.5eV`
The wavelength of radiation required to excite `Li^(++)`from the first orbit to the third orbit is given by
`(hc)/(lambda) = E_(0) - E_(1)`
`lambda= (hc)/(E_(0) - E_(1))`
`= (1242 eVnm)/(1088eV) = 11.4nm`
(b) The spectral lines emittedare due to the transition
`n = 3 rarr n = 2, n= rarr n = 1 and n= 2 rarr n = 1`Thus there will be three spectral lines in the spectrum