Question

(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?

Answer 1

(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.