The Balmer equation can be used to calculate the wavelengths of the spectral lin

Question

The Balmer equation can be used to calculate the wavelengths of the spectral lines in the visible region of the electromagnetic spectrum for the H atom. These lines are called the Balmer series and are produced by electron transitions from higher energy levels to the n = 2 energy level. Balmer's equation in terms of the frequency of the spectral lines is: %u03BD = 3.29 x 1015 s-1 (1/22 - 1/n2), where %u03BD is the frequency of the line and n is the higher energy level. Using the Balmer equation, calculate the wavelength of light in nanometers for the transition from n = 3 to n = 2.

Explanation / Answer

v (frequency) = 3.29*10^(15) (1/4- 1/n^2) s^(-1)

For n=3 to 2 transition n =3

v = 3.29*10^(15) (1/4- 1/3^2) s^(-1)

= 3.29*10^(15) * (5/36) s^(-1)

now

c = lambda * v

lambda = c/v

= 3*36*10^(8) /(3.29*10^(15) *5) m

= (3*36)/(3.29*5) *10^(-7) m

= 6.565 *10^(-7) m

= 656.5 nm

wavelength = 656.5 nm

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