KVPY Sample Paper KVPY Stream-SX Model Paper-21

  • question_answer
     If the de Brogile wavelength of the electro in nth Bohr orbit in a hydrogenic atom is equal to \[1.5\pi {{a}_{0}}\](\[a{{ }_{0}}\] is Bohr radius), then the value of n/z. is;

    A) 0.40

    B) 1.50

    C) 1.0

    D) 0.75

    Correct Answer: D

    Solution :

    \[2\pi r=n\lambda \]
    \[\lambda =\frac{2\pi r}{n}=\frac{2\pi {{n}^{2}}{{a}_{0}}}{n\times Z}=2\pi \frac{n}{Z}{{a}_{0}}\]
    \[\lambda =1.5\pi {{\alpha }_{0}}\]
    \[\therefore \]      \[2\pi \frac{n}{Z}{{a}_{0}}=1.5\pi {{\alpha }_{0}}\]\[\Rightarrow \]            \[\frac{n}{Z}=\frac{1.5}{2}=0.75.\]

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