Q155 / 160 · TS EAMCET 2023 (14 May Shift 2) · Physics

The ratio of longest wavelengths of the spectral lines in the Lyman and Balmer series of hydrogen spectrum is

  • A
    $\frac{3}{23}$
  • B
    $\frac{5}{27}$
  • Correct answer
    C
    $\frac{7}{29}$
  • D
    $\frac{9}{31}$

Solution

The longest wavelength for Lyman series $(2 \rightarrow 1)$ $\frac{1}{\lambda_{\mathrm{L}}}=\mathrm{R}\left(\frac{1}{(1)^2}-\frac{1}{(2)^2}\right)=\frac{3}{4} \mathrm{R}$ And for Balmer series $(3 \rightarrow 2)$ $\begin{aligned} & \frac{1}{\lambda_{\mathrm{B}}}=\mathrm{R}\left(\frac{1}{(2)^2}-\frac{1}{(3)^2}\right)=\frac{5}{36} \mathrm{R} \\ & \therefore \frac{\lambda_{\mathrm{L}}}{\lambda_{\mathrm{B}}}\end{aligned}$

Hence, the correct answer is option: 'C'.

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