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Atoms and Nuclei question

2018 · Shift 0 · Q69
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Atoms and Nuclei question

2018 · Shift 0 · Q69

JEE MainPhysicsAtoms and NucleiMCQ+4 / −1
If the series limit frequency of the Lyman series is uL{ u _L}uL​, then the series limit frequency of the Pfund series is:
  1. A
    uL/25{ u _L}/25uL​/25
  2. B
    25uL25{ u _L}25uL​
  3. C
    16uL16{ u _L}16uL​
  4. D
    uL/16{ u _L}/16uL​/16
View written solutionFree

Correct answer: A

  1. Use the hydrogen spectral frequency formula

For hydrogen, the frequency of a spectral line is

u = cR\left(\frac{1}{n_1^2}-\frac{1}{n_2^2}\right), \qquad n_2>n_1$$ For the **series limit**, $n_2 \to \infty$, so $$\nu_{\text{limit}} = cR\left(\frac{1}{n_1^2}-0\right)=\frac{cR}{n_1^2}$$ 2. **Lyman series limit** For the Lyman series, $n_1=1$. So, $$\nu_L = \frac{cR}{1^2}=cR$$ 3. **Pfund series limit** For the Pfund series, $n_1=5$. Hence, $$\nu_P = \frac{cR}{5^2}=\frac{cR}{25}$$ Using $\nu_L=cR$, $$\nu_P = \frac{\nu_L}{25}$$ 4. **Match with options** Thus the correct option is $$\boxed{\frac{\nu_L}{25}}$$ So, **Option A** is correct.
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