Wavelengths of the first lines of the Lyman series, Paschen series and Balmer series, in hydrogen spectrum are denoted by \[{{\lambda }_{L}},{{\lambda }_{P}},{{\lambda }_{B}}\] respectively. Arrange these wavelengths in increasing order.

Hint: Lyman, Balmer and Paschen series are a set of wavelengths of the spectral series for the hydrogen atom. When an electron in the hydrogen atom absorbs energy, it jumps into a higher orbital but that state is a metastable short life and it jumps back to the lower energy state. In this process energy is released and the wavelengths we get is divided into a set of spectra called spectral series.

Complete step by step solution:
- When an electron jumps from n=2,3,4,5,6,7 to n=1 then the series obtained is called Lyman series. The wavelength of the Lyman series is (90-120) nm.
- When an electron jumps from n=3,4,5,6,7 to n=2 then the series obtained is called the Balmer series. The wavelength of the Balmer series is (360-650) nm.
- When an electron jumps from n=4,5,6,7 to n=3 then the series obtained is called the Paschen series. The wavelength of the Paschen series is (820-1870) nm.
- We need to arrange the wavelengths of the first lines of Lyman, Balmer and Paschen series in increasing order and from the data above mentioned the answer comes out to be \[{{\lambda }_{L}},{{\lambda }_{P}},{{\lambda }_{B}}\] in ascending order respectively.

Note: The series we know are Lyman, Balmer, Paschen, Brackett and Pfund. There are more unnamed series, which follow the spectral pattern described by the Rydberg equation. These series are observed and have very high wavelengths. As we move upwards the spectral line becomes thinner and very difficult to observe.