When Balmer found his famous series for hydrogen in 1886, he was limited experim

Question

When Balmer found his famous series for hydrogen in 1886, he was limited experimentally to wavelengths in the visible and near regions from 250 nm to 700 nm, so all the lines in his series lie in that region. On the basis of the entries in Table 11.3 and the transitions on your energy level diagram, what common characteristic do the lines in the Balmer series have? What would be the longest possible wave for a line in the Balmer series? What would be the shortest possible wavelength that a line in the Balmer series could have? Fundamentally, why would any in the hydrogen spectrum between 250 nm and 700 nm belong to the Balmer series?

Explanation / Answer

The Balmer series is the name given to a series of spectral emission lines of the hydrogen atom that result from electron transitions from higher levels down to the energy level with principal quantum number 2

Longest possible wavelength have the lowest energy

The transition from 3rd to 2nd energy state has loowest energy in thses series

E = -13.6 /n^2

delta E = -13.6 [ 1/3^2 - 1/2^2] = 1.89 eV

1 eV = 1.6*10^-19 J

1.89 eV = 3.024*10^-19 J

E = hc / wavelength ; h = plancks constant , c= speed of light

Wavelength = hc /E = 6.57*10^-7 m = 657 nm

Shortest wavelength is the transition from infinity to 2nd state

delta E = -13.6 * [ 0^2 - 1/4 ] = 3.4 eV

3.4 eV = 5.44*10^-19 J

E = hc / wavelength

Wavelength = 365 nm

As the wavelength range from 365 nm to 657 nm is in balmer series

The range given is present in these region only , so the spectral lines are consider as Balmer series

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