Question

In a hydrogen spectrum if an electron moves from $ 7 $ to $ 1 $ orbit by transition in multi steps then find out the total number of lines in the spectrum.

Answer 1

Hint :We know that to solve this question we must recall the concepts of the Hydrogen spectrum. We should remember that the number of spectral lines of a particular series were the all possible transitions from a higher energy level to the energy level corresponding to that particular series.

Complete Step By Step Answer:
The wavelengths of emitted light depend on the energy difference between the two levels. In a pure sample of hydrogen gas, the emission spectrum looks like distinct lines of discrete wavelengths that are absolutely specific to the element hydrogen.
Some of these lines lie in the visible range of the electromagnetic spectrum, while others lie in the ultraviolet or infrared range. The series of visible lines in the hydrogen atom spectrum is called the Balmer series. This series of spectral emission lines occur when the electron transitions from a high-energy level to the lower energy level. Here we know that;
Lyman $ =\left( n7-1 \right)=7-1=6 $
Balmer $ =\left( n7-2 \right)=7-2=5 $
Paschen $ =\left( n7-3 \right)=7-3=4 $
Bracket $ =\left( n7-4 \right)=7-4=3 $
Pfund $ =\left( n7-5 \right)=7-5=2 $
Humphrey $ =\left( n7-6 \right)=7-6=1 $
Total $ =\text{ }21 $ , thus the total number of lines can be calculated as follows :
Therefore, the total number of lines $ 21. $

Note :
Remember that the other lines in the hydrogen spectrum. The Lyman series involves jumps to or from the ground state, the Paschen series to $ n=3 $ , the Brackett series to $ n=4 $ , and the Pfund series to $ n=5 $ . While the Lyman series is in the ultraviolet, Paschen, Brackett, Pfund, and Humphreys series are in the infrared region.