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

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.

Step-by-step explanation

lets calculate -

Rydberg equation-
`(1)/(\pi ) =R((1)/(n_1^2) -(1)/(n_2^2))`

where ,
`\pi` is wavelength , R is Rydberg constant (
`1.097*10^7`),
`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,

`(1)/(\pi )=1.097*10^7*((1)/(2^2) -(1)/(4^2) )`
`=2056875m^-^1`

Wavelength
`\pi =(1)/(2056875)`

=
`4.86*10^-^7` = 486nm

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