The ground state energy of hydrogen atom is - 13.6 eV. If an electron makes a transition from an energy level - 0.85 eV to -3.4 eV, calculate the wavelength of the spectral line emitted. To which series of hydrogen spectrum does this wavelength belong?

Explanation

The ground state energy of hydrogen `E_(1)` = 13.6 eV .
`therefore ` Energy `E_(i) = -0.85e V` corresponds to a level `n_(i)` where ` - 0.85 = (-13.6)/(n_(i)^(2)) rArr n_(i) = 4`
Again energy `E_(f) = - 3.4` eV corresponds to a level `n_(f)` such that ` -3.4 = - (13.6)/(n_(f)^(2))` , which leads us to the result `n_(f) = 2`
As transition is taking place from `n_(i) = 4` level to `n_(f) = 2` level the wavelenght belongs to Balmer series of hydrogen spectrum .
The wavelenght of spectrall line is given by the relation.
`hv = (hc)/(lambda) = E_(i) = E_(f) = - 0.85 eV - (-3.4 eV) = + 2.55 eV`.
`therefore " " lambda = (hc)/(2.55ev) = (6.63 xx 10^(-34) xx 3 xx 10^(8))/((2.55 xx 1.60 xx 10^(-19))J) = 4.875 xx 10^(-7) m = 487.5` nm