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Structure of Atom — Chemistry STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceChemistryStructure of Atom5 Marks
Question
  1. Calculate the wavelength and frequency of limiting line of Lyman series (Rydberg constant = $109677 \mathrm{~cm}^{-1}$)
  2. Give quantum numbers for electrons with highest energy in sodium atom (Z = 11)
  3. Which of the following sets of quantum numbers are not possible? Give reasons:
  1. $\text{n} =1,1=0,\text{m}_1=0,\text{m}_\text{s}=-\frac{1}{2}$
  2. $\text{n}=0,1=0,\text{m}_1=0,\text{m}_\text{s}=-\frac{1}{2}$
✓

Answer

  1. For lyman series $\text{n}_1-1\text{ n}_2=\infty$ for limiting line,
$\overline{\text{v}}=\frac{1}{\lambda}=\text{R}_\text{H}\Big(\frac{1}{\text{n}^2_1}=\frac{1}{\text{n}^2_2}\Big)$

$=109677\times\frac{1}{1^2}=109677\text{cm}^{-1}$

$\lambda=\frac{1}{109677}\text{cm}$

$=9.118\times10^{-6}\text{cm}$

$=9.118\times10^{-8}\text{m}$

Frequency(v),

$=\frac{\text{Velocity(c)}}{\text{Wavelength}(\lambda)}$

$\text{v}=\frac{3\times10^8\text{ms}^{-1}}{9.118\times10^{-8}\text{m}}=0.29\times10^{16}\text{s}^{-1}$

$\text{v}=3.29\times10^{15}\text{s}^{-1}$
  1. $\text{Na}(11):1\text{s}^2\ 2\text{s}^2\ 2\text{p}^6\ 3\text{s}^1$
$\text{n}=1,1=0,\text{m}=0,\text{s}=+\frac{1}{2}$
  1. (ii) is not possible because $\text{n}\not=0$ i.e., n cannot be equal to zero.

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