Calculate the value of ni for Hydrogen if a violet line from the Balmer series has a recorded wavelength of 410 nm.

Solution :

Given that the violet line from Balmer series having a recorded wavelength of 410 nm. As the recorded wavelength is 410 nm we know, the wavelength range of violet light is 380 nm -450 nm. So the 410 nm is corresponding to violet light wavelength.

We know, among all the series of lines spectrum of atom, only the Balmer series are in visible range. For Balmer series, the equation of wavelength associated with the e-transition of n = 2 orbit to n > 2 is

where, R = Rydberg constant = 109678 per cm

            λ = wavelength

Here the recorded λ = 410 nm =

∴

≈ 36

n = ±6

Here, n is the principle quantum number. It cannot be negative, so the value of n = 6 for hydrogen atom if the violet line from Balmer series that has a recorded wavelength of 410 nm.