Question

When the electron of $ 5th $ orbit jumps into the second orbit, the number of spectral lines produced in hydrogen spectrum is:

Answer 1

Hint :We know that Balmer series is a series of spectrum emission lines of hydrogen atom which results when electron transition occurs from higher level down to energy level with principal quantum number, Paschen series is a series of spectrum emission lines of hydrogen atom which results when electron transition occurs from higher level down to energy level with principal quantum number.

Complete Step By Step Answer:
When a substance absorbs energy, it emits radiation. Spectrum of such radiation is called the emission spectrum. Atoms, molecules or ions that absorb radiation are called excited. Spectrum of visible light is continuous. Spectrum of atoms in gaseous state does not show a continuous spectrum but they emit light at specific wavelengths with dark spaces between them.
Such a spectrum is called line spectrum or atomic spectrum. Line emission spectrums are important to understand electronic structure. Each element has a unique line emission spectrum. When an electric discharge is passed through gaseous hydrogen, hydrogen molecules dissociate and energetically excited hydrogen atoms produce electromagnetic radiation of discrete frequencies. The Hydrogen spectrum consists of several series of lines named after discoveries.
The electron jumps from fifth orbit to second orbit; $ {{n}_{1}}=5,{{n}_{2}}=2. $
The predefined formula for number of spectral lines is given by the formula, $ \dfrac{\left( {{n}_{1}}-{{n}_{2}} \right)\left( {{n}_{1}}-{{n}_{2}}+1 \right)}{2}=\dfrac{\left( 5-2 \right)\left( 5-2+1 \right)}{2}=6. $
Therefore, the electron of $ 5th $ orbit jumps into the second orbit, the number of spectral lines produced in the hydrogen spectrum is $ 6. $

Note :
Remember that the spectrum of visible light is continuous. Spectrums of atoms in gaseous state do not show continuous spectrum but they emit light at specific wavelengths with dark spaces between them. Such a spectrum is called line spectrum or atomic spectrum. Balmer showed when spectral lines are expressed in terms of wavenumber.