For a hydrogenic ion kinetic energy of electron in its `3^(rd)` excited state is found to be `54.4 eV`. Then series limit `((1)/(lamda))` for Balmer series, for this ion, is -

Options

A. `109678 xx 16 cm^-1`
B. `109678//16 cm^-1`
C. `109678 xx 4 cm^-1`
D. `109678 xx 64 cm^-1`

Answer

A

Explanation

(a) `KE = 13.6 = (Z^2)/(n^2) eV//"atom"`
`rArr 54.4 = 13.6 xx (Z^2)/(4^2)`
`rArr Z_2 = 64`
for Balmer series -
`(1)/(lamda) = RZ^2 [(1)/(2^2) -(1)/(oo^2)]` (for series limit)
=`109678 xx 64 [(1)/(4) -(1)/(oo)]`
`cm^-1 = 109678 xx 16 cm^-1`.