Question

Problem 8: Consider the Balmer series of spectral lines in the hydrogen atom. Part (a) What is the smallest-wavelength line, in nanometers, in the Balmer series? Numeric : A numeric value is expected and not an expression. Amin Part (b) Which part of the electromagnetic spectrum is this photon? MultipleChoice: 1) Gamma ray 2) Infrared 3) X-ray 4) Visible 5) Ultraviolet

Answer 1

For a transition from state ni to nf the wavelength of light emitted is given by

$\frac{1}{\lambda}=R\left ( \frac{1}{n_f^2}-\frac{1}{n_i^2} \right )$

R is the Rydberg constant

a) For smallest wavelength of Balmer series ni=infinity and nf=2

Putting the values,

L = 1.097 x 107 ( Amin

or, min = 3.646 x 10-' m = 364.6 nm

b) The UV spectrum has a wavelength of range10 nm to 400 nm.

So the shortest wavelength of Balmer series lies in the UV region.