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  • In Palmer series, wavelength of first line is and in Bracket t series wavelength of first line is <img alt=

In Palmer series, wavelength of first line is \lambda_1 and in Bracket t series wavelength of first line is \lambda_2. Then \frac{\lambda_1}{\lambda_2} is
 

Option: 1

 0.162
 


Option: 2

 0.124
 


Option: 3

 0.138
 


Option: 4

 0.158


Answers (1)

best_answer

Case-I

\begin{aligned} &\mathrm{ \frac{1}{\lambda_1}=R\left[\frac{1}{2^2}-\frac{1}{32}\right] }\\ &\mathrm{ \frac{1}{\lambda_1}=R\left[\frac{1}{4}-\frac{1}{9}\right]=\frac{5 R}{36}}\\ &\mathrm{\lambda_1=\frac{36}{5 R}}\\ \end{aligned}

Case - II

\begin{aligned} \frac{1}{\lambda_2} & =\mathrm{R\left[\frac{1}{4^2}-\frac{1}{52}\right] \Rightarrow R\left(\frac{1}{16}-\frac{1}{25}\right) }\\ \frac{1}{\lambda_2} & =\mathrm{\frac{9 R}{400}-(2) }\\ \therefore \frac{\lambda_1}{\lambda_2} & =\mathrm{\frac{36}{5 R} \times \frac{9 R}{400}} \\ \frac{\lambda_1}{\lambda_2} & =\mathrm{\frac{81}{5 \times 100}=\frac{16.2}{100}} \\ \frac{\lambda_1}{\lambda_2} & =0.162 \end{aligned}

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