Find the value of wave number $(\overline{\mathrm{v}})$ in terms of Rydberg's constant, when transition of…

Find the value of wave number $(\overline{\mathrm{v}})$ in terms of Rydberg's constant, when transition of electron takes place between two levels of $\mathrm{He}^{+}$ ion whose sum is 4 and difference is 2 .
  1. $\frac{8 \mathrm{R}}{9}$
  2. $\frac{32 \mathrm{R}}{9}$
  3. $\frac{3 \mathrm{R}}{9}$
  4. None of these

Solution

$\mathrm{n}_{1}+\mathrm{n}_{2}=4 ; \mathrm{n}_{2}-\mathrm{n}_{1}=2 ; \therefore \mathrm{n}_{1}=1, \mathrm{n}_{2}=3$
$\overline{\mathrm{v}}=\mathrm{R}(2)^{2}\left[\frac{1}{1^{2}}-\frac{1}{3^{2}}ight]=\frac{32 \mathrm{R}}{9}$ .

Asked in: JEE-TOPICTESTS-CHEMISTRY

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