JEE Main & Advanced Chemistry Structure of Atom / परमाणु संरचना Question Bank Self Evaluation Test - Structure of Atom

  • question_answer
    If the radius of first orbit of H atom is \[{{a}_{0}}\]the de- Broglie wavelength of an electron in the third orbit is                   

    A) \[4\pi {{a}_{0}}\]

    B) \[8\pi {{a}_{0}}\]

    C) \[6\pi {{a}_{0}}\]

    D) \[2\pi {{a}_{0}}\]

    Correct Answer: C

    Solution :

    [c] \[{{r}_{n}}={{a}_{0}}{{n}^{2}}\] \[r={{a}_{0}}\times {{(3)}^{2}}=9{{a}_{0}}\] \[mvr=\frac{nh}{2\pi };\] \[mv=\frac{nh}{2\pi r}=\frac{3h}{2\pi \times 9{{a}_{0}}}=\frac{h}{6\pi {{a}_{0}}}\] \[\lambda =\frac{h}{mv}=\frac{h}{h}\times 6\pi {{a}_{0}}=6\pi {{a}_{0}}\]


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