Question

Calculate the wavelength for the transition from n = 4 to n = 2, and state the name given to the spectroscopic series to which this transition belongs?

Answer 1

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-   $\frac{1}{\pi } =R(\frac{1}{n_1^2} -\frac{1}{n_2^2})$

where ,$\pi$ is wavelength , R is Rydberg constant ( $1.097\times10^7$), $n_1$ and $n_2$are the quantum numbers of the energy levels. (where $n_1=2 , n_2=4$)

Now putting the given values in the equation,

                $\frac{1}{\pi }=1.097\times10^7\times(\frac{1}{2^2} -\frac{1}{4^2} )$$=2056875m^-^1$

    Wavelength $\pi =\frac{1}{2056875}$

             =$4.86\times10^-^7$ = 486nm

   Therefore , the wavelength is 486nm and it belongs to The Balmer series.