JEE Main & Advanced Physics Nuclear Physics And Radioactivity Question Bank Critical Thinking

  • question_answer
    In the Bohr model of the hydrogen atom, let R, v and E represent the radius of the orbit, the speed of electron and the total energy of the electron respectively. Which of the following quantity is proportional to the quantum number n        [Pb. PET 2001; KCET 2002]

    A)            R/E

    B)            E/v

    C)            RE  

    D)            vR

    Correct Answer: D

    Solution :

               Rydberg constant \[R=\frac{{{\varepsilon }_{0}}{{n}^{2}}{{h}^{2}}}{\pi mZ{{e}^{2}}}\]                    Velocity \[v=\frac{Z{{e}^{2}}}{2{{\varepsilon }_{0}}nh}\] and energy \[E=-\frac{m{{Z}^{2}}{{e}^{4}}}{8\varepsilon _{0}^{2}{{n}^{2}}{{h}^{2}}}\]                    Now, it is clear from above expressions   R.v µ n


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