MCQ
What is the maximum wavelength line in the Lyman series of $He^+$ ion ?
  • A
    $3R$
  • $1/3R$
  • C
    $4/4R$
  • D
    None of these

Answer

Correct option: B.
$1/3R$
b
For $He ^{+}, Z =2$

Wave number, $\bar{v}=\frac{1}{\lambda}=R Z^2\left[\frac{1}{n_1^2}-\frac{1}{n_2^2}\right]$

For Lyman series, $n _1=1$ and for maximum wavelength, $n _2$ has to be the smallest possible energy level.

$\therefore n _2=2$

Therefore,

$\frac{1}{\lambda_{\max }}=4 R \left[\frac{1}{1}-\frac{1}{4}\right]$

$\Rightarrow \lambda_{\max }=\frac{1}{3 R }$

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