Question

Number of spectral lines in Balmer series when an electron return from ${{7}^{th}}$ orbital to ${{1}^{st}}$ orbital of Hydrogen atom are:
A) 5
B) 6
C) 21
D) 15

Answer 1

Hint: In the Hydrogen spectrum, the number of spectral lines possible will be equal to the number transitions possible between the highest orbital and the first orbital for the specified series.
For Balmer series n=2

Complete step by step answer:
To solve this question, we should have an idea about the emission spectra of Hydrogen.
We know that in an atom there will be many atoms and the atoms by absorbing the energy makes transitions to the higher energy level and as electrons are unstable in the excited state it comes back to the ground state or original state by the release of energy in the form of light or radiation and this phenomenon is accounts for emission spectrum.
Emission spectrum of a Hydrogen atom is called the Hydrogen emission spectrum.
In the Hydrogen emission spectrum there are various spectral line series which are classified by the wavelengths obtained by solving Rydberg's equation.
So the various spectral line series in Hydrogen are –Lyman series, Balmer series, Paschen series, Brackett series, Pfund series
Now let’s solve the question given.
In the question it is given that, we have to find the number of spectral lines in Balmer series when an ${{e}^{-}}$ returns from the ${{7}^{th}}$ orbital to ${{1}^{st}}$ orbital of Hydrogen atom.
We know that the Balmer series is the second series in the Hydrogen spectrum so the initial energy state or the orbital from which the higher transitions occurs is, n=2.
So for calculating the equation we use the formulae,
$N=\left( {{n}_{2}}-{{n}_{1}} \right)$
Where N is the total number of spectral lines possible for a spectral series.
${{n}_{2}}$= highest energy level and ${{n}_{1}}$ is the lowest energy level from which the transition occurs.
We know that here,${{n}_{2}}$=7 and ${{n}_{1}}$=2
Substitute these values in the above equation,
$N=\left( 7-2 \right)$
$N=5$
So the number of spectral lines in the Balmer series when an electron return from ${{7}^{th}}$orbital to ${{1}^{st}}$ orbital of Hydrogen atom is 5.

Hence the correct option from the given options is option (A).

Note: The ${{n}_{1}}$ value for Lyman series is n=1, for Balmer series n=2, Paschen series n=3, Brackett series n=4, Pfund series n=5.
The Lymann series lies in the UV range, Balmer series lies in visible range, Pascheen, Brackett and Pfund lie in the Infrared-red region.