Question

The Balmer series of hydrogen spectrum lies in:
(A) visible region spectra
(B) ultra violet spectra
(C) infrared region spectra
(D) \[\gamma \]-rays spectra

Answer 1

Hint: Visible region spectrum lies between 400 nm to 780 nm. Ultraviolet spectra lie between 100 nm to 400 nm. Infrared region spectrum lies between 700 nm to 1mm. \[\gamma \]-rays spectra are observed at a wavelength of less than 0.01 nm.

Complete step by step solution:
-Balmer series is named after the Swiss teacher Johann Balmer (1825-1898) in 1885, which is a series of spectral emission lines of the hydrogen atom that result from the transitions of electrons from higher levels to the energy level with principal quantum number 2.
-Balmer gave a general formula, by trial and error, which could describe spectra from other elements while he was studying simple spectral patterns was the lightest atom, hydrogen. The individual lines in the Balmer series were given particular names as Alpha, Beta, Gamma, and Delta, each corresponding to a \[{{n}_{i}}\] value of 3, 4, 5, and 6 respectively. Balmer concentrated on these four numbers only, and gave the formula:
\[\dfrac{1}{\lambda }=b\left[ \dfrac{1}{{{2}^{2}}}-\dfrac{1}{{{n}_{i}}^{2}} \right]\]
-Johannes Robert Rydberg then later in 1889, found several series of spectra that would fit a more general relationship which was similar to Balmer’s empirical formula, came to be known as the Rydberg formula. It is given by:
\[\dfrac{1}{\lambda }=R\left[ \dfrac{1}{{{n}_{f}}^{2}}-\dfrac{1}{{{n}_{i}}^{2}} \right]\,\,\,{{n}_{i}}>{{n}_{f}}\]
 where, \[{{n}_{i}}\] and \[{{n}_{f}}\] = 1, 2, 3, 4, 5, ….
 R (Rydberg constant) =\[1.097\times {{10}^{7}}{{m}^{-1}}\]
For the hydrogen atom, \[{{n}_{i}}\] = 2 corresponds to the Balmer series.

Name of Line	\[{{n}_{f}}\]	\[{{n}_{i}}\]	Wavelength	Colour
Balmer Alpha	2	3	656.28 nm	Red
Balmer Beta	2	4	486.13 nm	Teal
Balmer Gamma	2	5	434.05nm	Blue
Balmer Delta	2	6	410.17 nm	Indigo

From the above discussion, we can see these lie in the visible spectrum. So, the correct option is (A).

Note: There are other series in the hydrogen atom also.
-Lyman series with \[{{n}_{i}}\] = 1, present in the ultraviolet lines.
-Paschen series with \[{{n}_{i}}\] = 3, present in the infrared region of the spectrum.
-Brackett and Pfund series corresponding to \[{{n}_{i}}\] = 4 and \[{{n}_{i}}\] = 5 respectively, present in the infrared region.