Hydrogen Line Spectra
Hydrogen Line spectra – Bohr’s Model Approach
According to the third postulate of Bohr’s Model, whenever an electron jumps from higher energy level (orbit) of a Hydrogen atom to one of its lower energy level, an electromagnetic wave (em wave) emits. The energy of em wave is equal to the energy difference between the two energy levels. Mathematically, \[E_{if} = E_i – E_f \] where \(E_{if}\) is the energy of the electrmagnetic wave, \(E_i\) is the energy of the initial energy level (higher energy orbit) and \(E_f\) is the energy of the final energy level (lower energy orbit).
As the energy of each em wave emitted depends on the enrgy levels which have fixed energies, \[E_n = -\frac{13.6}{n^2}eV\], the energy associated with these em waves are discrete. Also, as energy of the em wave depends on its frequency, \[h \nu_{if} = E_{if} = E_i – E_f \]
\[h \nu_{if} =-13.6 (\frac{1}{{n_i}^2}-\frac{1}{{n_f}^2})\]
When the electrons jump from the excited states to ground states or other lower energy states, em waves of various frequencies are emitted. These are in the range of ultraviolet rays (Lyman Series), Visible Rays (Balmer Series), Infrared rays (Paschen Series) and so on.
