Question

Explain the different types of spectral series in a hydrogen atom.

Answer 1

According to Bohr, when an electron from its initial stationary orbit with $n=n_i$ jumps to another (lower) stationary orbit with $n=n_f$, it emits energy equal to the difference between the energy of the two stationary orbits in the form of small packets of light known as photons. For every transition of the electron, there is a line in the spectrum and there are different types of spectral series formed. He gave the spectrum of Hydrogen ion which has one electron only, so this spectrum cannot be applied for atoms with more than one electron. The following are the series in the hydrogen spectrum: –

a) Lyman Series: – when the electron jumps from any higher stationary orbit to first stationary orbit, the spectral lines falls in the Lyman series. For Lyman series, $n_i=1$.

Now putting $n_f=1$ in the relation given by Bohr,$w=R_h(\frac{1}{1^2}-\frac{1}{n_i^2})$, $n_i=2,3,\mathrm{4....}$

b) Balmer Series: – when the electron jumps from any higher stationary orbit to the second stationary orbit with $n_f=2$, the spectral lines falls in the Balmer Series. Here, $n_i=2$

$w=R_h(\frac{1}{2^2}-\frac{1}{n_i^2})$, $n_i=3,4,\mathrm{5....}$

c) Paschen Series: – when the electron falls from any higher stationary orbit to third stationary orbit with $n=3$, the spectral lines falls in the Paschen Series. Here $n_f=3$

$w=R_h(\frac{1}{3^2}-\frac{1}{n_i^2})$, $n_i=4,5,\mathrm{6....}$

d) Brackett Series: – when the electron jumps from any higher stationary orbit to fourth stationary orbit with n=4, the spectral lines fall in Bracket Series. Here, $n_f=4$

$w=R_h(\frac{1}{4^2}-\frac{1}{n_i^2})$, $n_i=5,6,\mathrm{7....}$

e) Pfund Series: – when the electron from any higher stationary orbit jumps to fifth stationary orbit with n=5, the spectral lines falls in Pfund Series. Here, $n_f=5$

$w=R_h(\frac{1}{5^2}-\frac{1}{n_i^2})$, $n_i=6,7,\mathrm{8....}$