(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 observed in the emission spectrum of the above excited system?

Explanation

(a) The enrgy in the first orbit `=E_(1)=Z^(2)E_(0)` where `E_(0)= -13.6 eV` is the energy of a hydrogen atom in ground state thus for `Li^(++)`,
`E_(1)=9E_(0)=9xx(-13.6eV)= -122.4 eV`
The energy in the third orbit is
`E_(3)=(E_(1))/(n^(2))=(E_(1))/(9)= -13.6 eV`
Thus, `E_(3)-E_(1)=8xx13.6eV=108.8 eV`
Energy required to excite `Li^(++)` from the first orbit to the third orbit is given by
`E_(3)-E_(1)=8xx13.6eV=108.8eV`
The wavelength of radiation required to excite `Li^(++)` from the first orbit to the third orbit is given by
`(hc)/(lambda)=E_(3)-E_(1)`
or, `lambda=(hc)/(E_(3)-E_(1))`
`(1240eV0nm)/(108.8eV)~~11.4 nm`
(b) The spectral lines emiited are due to the transitions `n=3 rarrn=2,n=3rarrn=1` and `n=2rarrn=1`. Thus, there will be three spectral lines in the spectrum.