Answer:
The wavelength for the transition from n = 4 to n = 2 is 486nm and the name name given to the spectroscopic series belongs to The Balmer series.
Explanation
lets calculate -
Rydberg equation- [tex]\frac{1}{\pi } =R(\frac{1}{n_1^2} -\frac{1}{n_2^2})[/tex]
where ,[tex]\pi[/tex] is wavelength , R is Rydberg constant ( [tex]1.097\times10^7[/tex]), [tex]n_1[/tex] and [tex]n_2[/tex]are the quantum numbers of the energy levels. (where [tex]n_1=2 , n_2=4[/tex])
Now putting the given values in the equation,
[tex]\frac{1}{\pi }=1.097\times10^7\times(\frac{1}{2^2} -\frac{1}{4^2} )[/tex][tex]=2056875m^-^1[/tex]
Wavelength [tex]\pi =\frac{1}{2056875}[/tex]
=[tex]4.86\times10^-^7[/tex] = 486nm
Therefore , the wavelength is 486nm and it belongs to The Balmer series.
