Why there is a large number of lines in the hydrogen spectrum?

Hydrogen produces a line spectrum because electrons exist only in discrete, quantised energy levels. When electrons jump between these fixed energy states, they emit photons with specific energies (E = h? ). This creates distinct spectral lines instead of continuous wavelengths. Bohr's model explains this through quantised orbits. Classical physics, on the other hand, would predict a continuous spectrum.

The hydrogen emission spectrum contains several spectral series, each named after its discoverer.

• Lyman series (n' = 1): To ground state, visible only in ultraviolet region
• Balmer series (n' = 2): Transitions to second level, appearing in visible region
• Paschen series (n' = 3): Moved to third level, visible in the infrared region
• Brackett series (n' = 4): Transitions to fourth level, appearing in the far infrared region
• Pfund series (n' = 5): Transitions to fifth level, showing in the infrared region
• Humphreys series (n' = 6): Transitions to sixth level, appearing in the infrared region

Change in surface energy = work done

$\left|\Delta E_0\right|=\left(-136\left\{1-\frac{1}{4}\right\}\right)eV$

|DE₀| = –10.2

$\lambda =\frac{12400}{10.2}\times 10^{-10}m$

$\rho =\frac{h}{\lambda }=\frac{6.63\times 10^{-34}\times 10.2}{12400\times 10^{-10}}$                  

$?$ $mv=\frac{h}{\lambda }$            

  $1.8\times 10^{-27}$           

$v=\frac{6.63\times 10.2\times 10^{-34}}{12400\times 10^{-10}}$

$v=\frac{6.63\times 10.2}{12400\times 1.8}\times 10^3$            

$=\frac{6.63\times 102}{124\times 1.8}=3.02$ ]

= 3 m/s

$-0.85=\frac{-13.6}{n^2}$  

n = 4

Number of transitions = $\frac{4\times 3}{2}=6$