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

Answer

Correct option: B.
$\frac {32R}{9}$
b
Rydberg's formula is $\frac{1}{\lambda}=R Z^{2}\left(\frac{1}{n_{f}^{2}}-\frac{1}{n_{i}^{2}}\right) \quad \bar{V}=\frac{1}{\lambda}$

We have given that $n_{f}-n_{i}=2$ And $n_{f}+n_{i}=4$

Solving these equation $n_{f}=3 \quad n_{i}=1$

For helium, $Z=2-$

Using rydberg's formula, $\frac{1}{\lambda}=R \times 2^{2}\left(\frac{1}{1^{2}}-\frac{1}{3^{2}}\right)$

$\bar{v}=\frac{32 R}{9}$

Therefore, the answer is B.

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