(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`.

Options

A. 108.8 e V ,3
B. 13.6e V, 4
C. 54.4 e V, 2
D. 10.2 e V, 3

Answer

A

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) = 9 E_(0) =9xx (-13.6eV)`
The energy in the third orbit is
`E_(3) =( E_1)/( n^2) =( E_1)/(9) =-13.6eV`
Thus , `E_(3) - E_(1) = 108.8eV , (hc)/(lambda)= E_(a) - E_(1)` .