Atomic Physics Question 6
Question 6 - 31 January - Shift 1
For hydrogen atom, $\lambda_1$ and $\lambda_2$ are the wavelengths corresponding to the transitions 1 and 2 respectively as shown in figure. The ratio of $\lambda_1$ and $\lambda_2$ is $\frac{x}{32}$. The value of $x$ is_______
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Answer: (27)
Solution:
Formula: Wavelength Corresponding To Spectral Lines
$ \begin{aligned} & \begin{matrix} 1 \\ \lambda \end{matrix} =Rz^{2} \begin{bmatrix} 1 & 1 \\ n_1^{2} & -n_2^{2} \end{bmatrix} \\ & 1 \\ & \lambda_1=Rz^{2} \begin{bmatrix} 1 & 1 \\ 1^{2} & 3^{2} \end{bmatrix} = _9^{8} Rz^{2} \\ & 1=Rz^{2} \begin{bmatrix} 1 & 1 \\ 1^{2} & 2^{2} \end{bmatrix} = _4^{3} Rz^{2} \\ & \frac{1}{2} \Rightarrow \frac{\lambda_2}{\lambda_1}= _9^{8} \times _3^{4}= _27^{32} \\ & \frac{\lambda_1}{\lambda_2}=\frac{27}{32} \end{aligned} $
Ans. 27
