The ratio of the shortest wavelength of Balmer series to the shortest wavelength of Lyman series for…

The ratio of the shortest wavelength of Balmer series to the shortest wavelength of Lyman series for hydrogen atom is :
  1. $4: 1$
  2. $1: 4$
  3. $2: 1$
  4. $1: 2$

Solution


$\begin{aligned} & \frac{1}{\lambda}=\mathrm{Rz}^2\left(\frac{1}{\mathrm{n}_1^2}-\frac{1}{\mathrm{n}_2^2}\right) \\ & \frac{\frac{1}{\lambda_{\mathrm{L}}}=\mathrm{Rz}^2\left(\frac{1}{1^2}\right)}{\frac{1}{\lambda_{\mathrm{B}}}=\mathrm{Rz}^2\left(\frac{1}{2^2}\right)} \\ & \frac{\lambda_{\mathrm{B}}}{\lambda_{\mathrm{L}}}=4: 1\end{aligned}$

Asked in: JEE Main 2024 (06 Apr Shift 1)

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