`A` H-like ion is observed to emit six different wavelength originating from all possible transitions between a group of levels. These levels have energies between `-0.85 eV` (Min) and `-0.544 eV` (Max)
(a) Find atmoic number (z) of element
(b) Find quantum number of levels between which transitions occur.
(c) Calculate largest wavelength emitted in transitions between the levels.

Explanation

`implies ((n_(2)-n_(1))(n_(2)-n_(1)+1))/(2)=6`
`implies n_(2)-n_(1)=3….(i)`
`E_(n_(2))=-0.544eV=-13.6xx(Z^(2))/(n_(2)^(2))`
`E_(n_(1))=-0.85eV=-13.6xx(Z^(2))/(n_(1)^(2))=(0.85)/(0.544)=[(n_(2))/(n_(1))]^(2)=(25)/(16)implies(n_(2))/(n_(1))=(5)/(4)....(ii)`
(a)`-0.544=-13.6xx(Z^(2))/(15^(2))impliesZ=3`
(b) Solving (i) and (ii), `n_(2)=15 & n_(1)=12`
(c ) `(hc)/(lambda_(max))=E_(15)-E_(14)implies (1240)/(lambda(nm))=(-13.6xx3^(2))/(15^(2))+(13.6xx3^(2))/(14^(2))implieslambda_(max)=15406nm`