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WBJEE · Physics · Atomic Physics

If \(\mathrm{R}\) is the Rydberg Constant in \(\mathrm{cm}^{-1}\), then hydrogen atom does not emit any radiation of wave-length in the range of

  1. A \(\frac{1}{\mathrm{R}}\) to \(\frac{4}{3 \mathrm{R}} \mathrm{cm}\)
  2. B \(\frac{7}{5 \mathrm{R}}\) to \(\frac{19}{5 \mathrm{R}} \mathrm{cm}\)
  3. C \(\frac{4}{\mathrm{R}}\) to \(\frac{36}{5 \mathrm{R}} \mathrm{cm}\)
  4. D \(\frac{9}{\mathrm{R}}\) to \(\frac{144}{7 \mathrm{R}} \mathrm{cm}\)
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Answer & Solution

Correct Answer

(B) \(\frac{7}{5 \mathrm{R}}\) to \(\frac{19}{5 \mathrm{R}} \mathrm{cm}\)

Step-by-step Solution

Detailed explanation

Hint: \(\frac{1}{\lambda}=\mathrm{R}\left[\frac{1}{\mathrm{n}_{\mathrm{f}^{2}}}-\frac{1}{\mathrm{n}_{\mathrm{i}^{2}}}\right]\) For range of wavelengths:\(\mathrm{n}_{\mathrm{i}}=1,2,3, \ldots . .\) for Lyman, Balmer, Paschen, \(\ldots \ldots\)…