A) \[2\times {{10}^{7}}\]
B) \[2\times {{10}^{10}}\]
C) \[2\times {{10}^{14}}\]
D) None
Correct Answer: B
Solution :
[b] \[\because r\propto \frac{1}{m}\therefore \frac{{{r}_{{{\pi }^{-}}}}}{{{r}_{e}}}=\frac{{{m}_{e}}}{{{m}_{{{\pi }^{-}}}}}\] \[{{r}_{{{\pi }^{-}}}}=\frac{{{r}_{e}}{{m}_{e}}}{{{m}_{{{\pi }^{-}}}}}=1.94\times {{10}^{-13}}m\] \[\because V=\frac{{{e}^{2}}}{2{{\varepsilon }_{0}}h}=2.2\times {{10}^{6}}m/s\] \[\therefore {{T}_{{{\pi }^{-}}}}=\frac{2\pi {{r}_{{{\pi }^{-}}}}}{V}=5.6\times {{10}^{-19}}\sec \] \[\therefore n=\frac{{{10}^{-8}}}{{{T}_{{{\pi }^{-}}}}}\simeq 2\times {{10}^{10}}\]You need to login to perform this action.
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