Question

Taking Rydberg's constant $R_H=1.097\times 10^{7}m$ first and second wavelength of Balmer series in hydrogen spectrm, is :

• A. $2000\mathring{A},3000\mathring{A}$
• B. $1575\mathring{A},2960\mathring{A}$
• C. $6529\mathring{A},4280\mathring{A}$
• D. $6552\mathring{A},4863\mathring{A}$

Answer 1

Answer: (D)

The wavelength of the lines in Balmer series is represented by,
$\frac{1}{\lambda }=R_H\left[\frac{1}{2^2}-\frac{1}{n_2^2}\right]$
For first wavelength
$\frac{1}{{\lambda }_1}=1.097\times 10^7\left[\frac{1}{2^2}-\frac{1}{3^2}\right]$
$=1.524\times 10^{6}m$
or ${\lambda }_1=\frac{1}{1.524\times 10^6}$
$=6.562\times 10^{-7}$
or ${\lambda }_1=6562\mathring{A}$
For second wavelength
$\frac{1}{{\lambda }_1}=1.097\times 10^{-7}\left[\frac{1}{2^2}-\frac{1}{4^2}\right]$
$=2.056\times 10^6$
or ${\lambda }_2=\frac{1}{2.056\times 10^6}$
or ${\lambda }_2=4.863-7\times 10\times 10^{-10}$
or ${\lambda }_2=4863\mathring{A}$