KVPY Sample Paper KVPY Stream-SX Model Paper-13

  • question_answer
    For emission line of atomic hydrogen from \[{{n}_{i}}=8\] to \[{{n}_{i}}=\]the plot of wave number \[(\overline{v})\] against \[\left( \frac{1}{{{n}^{2}}} \right)\]will be (The Rydberg constant, \[{{\text{R}}_{H}}\] is in wave number unit).

    A) Linear with slope \[-{{\text{R}}_{\text{H}}}\]

    B) Linear with intercept \[-{{\text{R}}_{\text{H}}}\]

    C) None linear

    D) Linear with slope \[{{\text{R}}_{\text{H}}}\]

    Correct Answer: D

    Solution :

    \[\frac{1}{\lambda }\,=\,\bar{v}\,=\,\text{R}{{ & }_{H}}{{z}^{2}}\left( \frac{1}{\eta _{1}^{2}}\,-\,\frac{1}{\eta _{2}^{2}} \right)\]
    \[\bar{v}\,=\,{{\text{R}}_{H}}\times \left( \frac{1}{\eta _{1}^{2}}\,-\,\frac{1}{{{8}^{2}}} \right)\]
    \[\bar{v}\,=\,{{\text{R}}_{\text{H}}}\times \,\frac{1}{{{\eta }^{2}}}-\,\frac{{{\text{R}}_{\text{H}}}}{{{8}^{2}}}\,\]\[\Rightarrow \] \[\bar{v}\,=\,{{\text{R}}_{H}}\times \frac{1}{{{\eta }^{2}}}\,-\,\frac{{{\text{R}}_{H}}}{64}\]
    \[m={{R}_{H}}\]
    Linerar with slope \[{{\text{R}}_{\text{H}}}.\]


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