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NEET Physics Atomic Physics NEET PYQ-Atomic Physics

  • question_answer
    The wavelength of the first line of Lyman series for hydrogen atom is equal to that of the second line of Balmer series for a hydrogen like ion. The atomic number Z of hydrogen like ion is                                             [AIPMT (S) 2011]

    A)  4            

    B)  1

    C)                   2                    

    D)       3

    Correct Answer: C

    Solution :

    Lyman series for H-ion
    \[\frac{hc}{\lambda }=Rhc\left( \frac{1}{{{1}^{2}}}-\frac{1}{{{2}^{2}}} \right)\]
    and for H-like ion         
    \[\frac{hc}{\lambda }={{Z}^{2}}Rhc\left( \frac{1}{{{2}^{2}}}-\frac{1}{{{4}^{2}}} \right)\]
    \[\therefore \]      \[\left( \frac{1}{{{1}^{2}}}-\frac{1}{{{2}^{2}}} \right)={{Z}^{2}}\left( \frac{1}{4}-\frac{1}{16} \right)\]
    \[\left( 1-\frac{1}{4} \right)={{Z}^{2}}\left( \frac{1}{4}-\frac{1}{16} \right)\]
    \[Z=2\]


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