The shortest wavelength transition in the paschen series in hydrogen occurs at 821 nm. So, at what wavelength does it occur ain Li2+ (isoelectronic of hydrogen)??? The options for the above question are:- a) 91.2 nm , b)273.6 nm , c)821.0 nm , d)7389.o nm........... Which of the options is correct and how please explain in detail..

Ans: (a) 91.2 nm

The shortest wavelength transition in the Paschen series in hydrogen occurs at 821 nm. According to the equation, the allowed energies of one electron atoms and ions are propotional to Z², so we can expect the frequencies of the transitions between the same two levels to scale as Z² too. Because wavelength is inversely propotional to the frequency. It follows that the wavelength of the transition should scale as 1/Z². Therefore, the same transition in Li²⁺ (For which Z=3) can be expected to lie at = 91.2 nm