A line in the Balmer series of the emission spectrum of atomic hydrogen is observed at a wavelength of 486.3 nm. Deduce the upper state principal quantum number for this transition.

4

Explanation:

The Balmer series refers to to a series of spectral emission lines of the hydrogen atom that occurs when an electron moves from higher energy  levels to the energy level of n= 2.

Hence;

λ =  486.3 * 10^-9 m

RH = 1.097 * 10^7 m-1

nf = 2

ni = ?

Using the formula;

1/λ = RH (1/nf^2 - 1/ni^2)

1/486.3 * 10^-9 = 1.097 * 10^7 (1/4 - 1/ni^2)

2.06 * 10^6/1.097 * 10^7 = (1/4 - 1/ni^2)

0.188 = 1/4 - 1/ni^2

1/ni^2 = 1/4 - 0.188

1/ni^2 = 0.25 - 0.188

1/ni^2 = 0.062

ni^2 = 16

ni = 4