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CET Karnataka Engineering CET - Karnataka Engineering Solved Paper-2009

  • question_answer
     Hydrogen atom from excited state comes to the ground stage by emitting a photon of wavelength\[\lambda \]. If R is the Rydberg constant, the principal quantum number n of the excited state is

    A)  \[\sqrt{\frac{\lambda R}{\lambda R-1}}\]                            

    B)  \[\sqrt{\frac{\lambda }{\lambda R-1}}\]

    C)  \[\sqrt{\frac{\lambda {{R}^{2}}}{\lambda R-1}}\]                             

    D)  \[\sqrt{\frac{\lambda R}{\lambda -1}}\]

    Correct Answer: A

    Solution :

    Here, \[{{n}_{f}}=1,\,\,{{n}_{i}}=n\] \[\therefore \] \[\frac{1}{\lambda }=R\left( \frac{1}{{{1}^{2}}}-\frac{1}{{{n}^{2}}} \right)\Rightarrow \frac{1}{\lambda }=R\left( 1-\frac{1}{{{n}^{2}}} \right)\]   ? (i) or            \[\frac{1}{\lambda R}=1-\frac{1}{{{n}^{2}}}\]or \[\frac{1}{{{n}^{2}}}=1-\frac{1}{\lambda R}\] or                            \[n=\sqrt{\frac{\lambda R}{\lambda R-1}}\]       


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