The Line Spectra of the Hydrogen Atom
A hydrogen atom consists of an electron orbiting its nucleus. The electromagnetic force between the electron and the nuclear proton leads to a set of quantum states for the electron, each with its own energy. These states were visualized by the Bohr model of the hydrogen atom as being distinct orbits around the nucleusThe continuous spectrum of black-body radiation is emitted by all objects heated to high temperatures or otherwise supplied with sufficient energy -- a process called excitation. Any object which is not a perfect radiation source, or ideal black body, is also found to emit strongly at specific wavelengths in addition to its continuous spectrum emission. These specific wavelengths, which are sharply defined, are highly characteristic of the substance being excited; they are called line spectra. Isolated atoms, which are the form of matter found at extremely high temperatures, emit line spectra which are characteristic of the element whose atoms are being excited. Chemists make use of this to identify the elements present in samples; the technique is called emission spectroscopy.
In emission spectroscopy, a source of energy, usually heat as in a flame or an electric arc or spark, is passed into the sample, which absorbs such frequencies as are possible; the re-emission of this light by the sample is observed. The process of absorption and re-emission produces a bright line spectrum which can be measured when the light is dispersed by a grating or prism. The wavelengths of the emitted light identify the element and the particular electronic transition occurring within it. The amount of light emitted is related to the amount of the element present, and if sufficient precautions are taken the amount can be semiquantitatively determined by measuring the amount of this light. This can be done photographically or by more complex electronic procedures.
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, ni=1. Now putting nf=1 in the relation given by Bohr, w=RH(1/12 – 1/ni2), ni=2, 3, 4…
b. Balmer Series: –
when the electron jumps from any higher stationary orbit to the second stationary orbit with n=2, the spectral lines falls in the Balmer Series. Here, ni=2 W=RH (1/22 – 1/ni2), ni=3, 4, 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 nf=3 w= RH (1/32 – 1/ni2), ni=4, 5, 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, nf=4 w= RH (1/42 – 1/ni2), ni= 5, 6, 7…