According to Bohr's theory of hydrogen atom, the ratio of the maximum and minimum wavelength of Lyman series…

According to Bohr's theory of hydrogen atom, the ratio of the maximum and minimum wavelength of Lyman series will be
  1. $3: 4$
  2. $4: 3$
  3. $2: 5$
  4. $5: 2$

Solution

$\frac{1}{\lambda}=\mathrm{R}\left(\frac{1}{\mathrm{n}_1^2}-\frac{1}{\mathrm{n}_2^2}\right)$
For Lyman series, $\mathrm{n}_1=1$ $\begin{aligned} \quad \frac{1}{\lambda_{\max }} & =R\left(\frac{1}{1^2}-\frac{1}{2^2}\right)=\frac{3}{4} R \\ \frac{1}{\lambda_{\min }} & =R\left(\frac{1}{1^2}-\frac{1}{\infty^2}\right)=R \\ \therefore \quad & \frac{\lambda_{\max }}{\lambda_{\min }} \end{aligned}=\frac{4}{3}$

Asked in: MHT CET 2024 (09 May Shift 1)

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