Question

The first spectral line in the Pfund series of Hydrogen spectrum is given by $ (\,{R_H} = Rydberg\,cons\tan t\,) $ :
A. $ \dfrac{{56{R_H}}}{{36}} $
B. $ \dfrac{{7{R_H}}}{{144}} $
C. $ \dfrac{{11{R_H}}}{{900}} $
D. $ \dfrac{{9{R_H}}}{{400}} $

Answer 1

Hint :To know the first spectral line in the Pfund series of hydrogen spectrum by Rydberg constant, we should know the formula of Rydberg constant. And for the Rydberg constant, the first spectral line is 6.

Complete Step By Step Answer:
A series of wavenumber in the Pfund series of the Hydrogen spectrum is given by $ {R_H}[\dfrac{1}{{{5^2}}} - \dfrac{1}{{{n^2}}}] $ , where $ {R_H} $ si the Rydberg Constant for hydrogen and $ n $ is an integer greater than 5.
Now, the first spectral line $ n\, = 6 $ .
 $ \dfrac{1}{\lambda } = {R_H}[\dfrac{1}{{{5^2}}} - \dfrac{1}{{{6^2}}}] = {R_H}[\dfrac{1}{{25}} - \dfrac{1}{{36}}] = \dfrac{{11{R_H}}}{{900}} $
The spectral series is broken into corresponding series based on the electron transition to lower energy state. The greek alphabets are used within the series to segregate the spectral lines of corresponding energy. The spectral series of Hydrogen are: The series was discovered during the years 1906-1914, by Theodore Lyman.
Hence, the correct option is C. $ \dfrac{{11{R_H}}}{{900}} $

Note :
Now, a question arises here: why are spectral lines grouped into series? So, because the energy of each state is fixed, the energy difference between them is fixed, and the transition will always produce a photon with the same energy. The spectral lines are grouped into series according to $ n $ .