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JEE Main & Advanced Physics Atomic Physics Question Bank Self Evaluation Test - Atoms

  • question_answer
    Suppose an electron is attracted towards the k origin by a force \[\frac{k}{r}\] where A: is a constant and r is the distance of the electron from the origin. By applying Bohr model to this system, the radius of the nth orbital of the electron is found to be \['{{r}_{n}}'\] and the kinetic energy of the electron to be\['{{K}_{n}}'\]. Then winch of the following is true

    A)  \[{{K}_{n}}\] independent of n, \[{{r}_{n}}\propto n\]

    B)  \[{{K}_{n}}\propto \frac{1}{n},{{r}_{n}}\propto n\]

    C)  \[{{K}_{n}}\propto \frac{1}{n},{{r}_{n}}\propto {{n}^{2}}\]

    D)  \[{{K}_{n}}\propto \frac{1}{{{n}^{2}}},{{r}_{n}}\propto {{n}^{2}}\]

    Correct Answer: A

    Solution :

    [a] \[\frac{m{{v}^{2}}}{r}=\frac{K}{r}\text{ or }v=\sqrt{\frac{K}{m}}=cr{}^\circ \] Now \[mvr=\frac{nh}{2\pi }\text{ or }r=\frac{nh}{2\pi mv}\] \[\therefore r\propto n.\] Also kinetic energy \[K=\frac{m{{v}^{2}}}{2}=\frac{m}{2}\times \frac{K}{m}=\frac{K}{2}.\]


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