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JEE Main & Advanced Sample Paper JEE Main - Mock Test - 36

  • question_answer
    A pi-mesic hydrogen atom is a bound state of a charged pion (denoted by\[{{\pi }^{-}},{{m}_{{{\pi }^{-}}}}=273{{m}_{e}}\]) and a proton.. The number of revolution a \[{{\pi }^{-}}\] makes in ground state of atom before it decays (mean life of a\[{{\pi }^{+}}\simeq {{10}^{-8}}S\])

    A) \[2\times {{10}^{7}}\]         

    B)        \[2\times {{10}^{10}}\]

    C) \[2\times {{10}^{14}}\]         

    D)        None

    Correct Answer: B

    Solution :

    [b] \[\because r\propto \frac{1}{m}\therefore \frac{{{r}_{{{\pi }^{-}}}}}{{{r}_{e}}}=\frac{{{m}_{e}}}{{{m}_{{{\pi }^{-}}}}}\] \[{{r}_{{{\pi }^{-}}}}=\frac{{{r}_{e}}{{m}_{e}}}{{{m}_{{{\pi }^{-}}}}}=1.94\times {{10}^{-13}}m\] \[\because V=\frac{{{e}^{2}}}{2{{\varepsilon }_{0}}h}=2.2\times {{10}^{6}}m/s\] \[\therefore {{T}_{{{\pi }^{-}}}}=\frac{2\pi {{r}_{{{\pi }^{-}}}}}{V}=5.6\times {{10}^{-19}}\sec \] \[\therefore n=\frac{{{10}^{-8}}}{{{T}_{{{\pi }^{-}}}}}\simeq 2\times {{10}^{10}}\]


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