Q168 / 200 · Manipal (MET) 2014 · Physics

The ratio of the wavelength for $2 \rightarrow 1$ transition in $\mathrm{Li}^{+}, \mathrm{He}^{+}$and H is

  • A
    $1: 2: 3$
  • B
    $1: 4: 9$
  • Correct answer
    C
    $4: 9: 36$
  • D
    $3: 2: 1$

Solution

$\begin{aligned} & \text { Using } \frac{1}{\lambda}=R Z^2\left(\frac{1}{n_1^2}-\frac{1}{n_2^2}\right) \Rightarrow \lambda \propto \frac{1}{Z^2} \Rightarrow \\ & \lambda_{\mathrm{Li}}: \lambda_{\mathrm{He}}: \lambda_{\mathrm{H}}=\frac{1}{9}: \frac{1}{4}: \frac{1}{1}=4: 9: 36\end{aligned}$

Hence, the correct answer is option: 'C'.

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