Question

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

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

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 ${\lambda }_1=6562\stackrel{o}{A}$ 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 ${\lambda }_2=4863\stackrel{o}{A}$