(a) (i) Find the wavelength of the radiation required to excite thye elctron in `Li(++)` from the first to the third Bohr orbit.
(ii) How many spectal lines are observed in the emission spectrum of the above excited system ?
(b) The energy needed to detach the electron of a hydrogen-like ion in ground state in 4 rydberg.
(i) What is the wavelength of the radiation emitted when the electron jumps from the first excited state ot the ground state ?
(ii) What is the radius of first orbit ?
(c ) A hydrogen sample is prepared in a particular excited state A. Photons of energy 2.55 eV get absorbed into the sample to take some electrons to a further excited state B. Find the quantum number of the A and B.
(d) A hydrogen atom in a state having a binding energy of 0.85 eV makes transition to a state with excitation energy 10.2 eV. (i) Identify the quantum number n of the upper and the lower energy states.
Find `lambda`.

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^(++), Z=3 E_(1)=9E_(0)=9xx (-13.6eV)`
`E_(3)=(E_1)/(n^3)=(E_1)/(9)=-13.6eV`
Thus, `E_(3)-E_(1)=8xx 13.6eV =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)`
`lambda =(12375)/(108.8eV)(Å)` or `lambda =114Å`.
(b) The spectral lines emitted are due to the transition n
`=3 to n=2, n=3 to n =1 and n=2 to n=1`, thus there will be three spectral lines.