Q157 / 160 · AP EAMCET 2022 (06 Jul Shift 1) · Physics

The shortest wavelength in the Paschen series of the Hydrogen spectrum is Rydberg constant of hydrogen $=1.097 \times 10^7 \mathrm{~m}^{-1}$.

  • A
    $91.2 \mathrm{~nm}$
  • B
    $364.6 \mathrm{~nm}$
  • Correct answer
    C
    $820.4 \mathrm{~nm}$
  • D
    $2278.9 \mathrm{~nm}$

Solution

For shortest wavelength of Paschen series $\left(n_1=3\right.$, $\begin{aligned} & \left.\mathrm{n}_2=\infty\right) \\ & \frac{1}{\lambda_{\mathrm{S}}}=\mathrm{R}_{\mathrm{H}}\left(\frac{1}{3^2}-\frac{1}{\infty}\right) \\ & \lambda_{\mathrm{S}}=\frac{9}{\mathrm{R}_{\mathrm{H}}}=\frac{9}{1.097 \times 0^7} \mathrm{~m} \\ & =820.4 \mathrm{~nm} \end{aligned}$

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

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