JEE Main & Advanced Sample Paper JEE Main Sample Paper-38

  • question_answer 54) What is the ratio of the circumference of the first Bohr orbit for the electron in the hydrogen atom to the de Broglie wavelength of electrons having the same velocity as the electron in the first Bohr orbit of the hydrogen atom?

    A)  \[1:1\]                          

    B)  \[1:2\]

    C)  \[1:4\]                          

    D)  \[2:1\]

    Correct Answer: A

    Solution :

      \[mvr=\frac{nh}{2\pi },\lambda =\frac{h}{mv};\] Using the two concept we get, \[mvr=\frac{nh}{2\pi }\] (where \[n=1\])             \[2\pi r=\frac{1\times h}{mv}\]                                                                ??(1);             \[\lambda =\frac{h}{mv}\]                                                                             ??(2) Divide (2) by (1), \[\frac{2\pi r}{\lambda }=\frac{h\times mv}{mv\times h}=\frac{1}{1}=1:1\]

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