A) \[2.99\times {{10}^{-7}}\text{s}\]
B) \[2.99\times {{10}^{-8}}\text{s}\]
C) \[2.99\times {{10}^{-9}}\text{s}\]
D) \[2.99\times {{10}^{-10}}\text{s}\]
Correct Answer: C
Solution :
Electric force acting on an electron \[(F)=Fe\] Acceleration produced in electron \[a=\frac{F}{m}=\frac{Ee}{m}\] \[s=ut+\frac{1}{2}a{{t}^{2}}\] \[s=0+\frac{1}{2}a{{t}^{2}}\] \[\therefore \] \[t=\sqrt{\frac{2s}{a}}=\sqrt{\frac{2sm}{Ee}}\] \[=\sqrt{\frac{2\times 4\times {{10}^{-2}}\times 9\times {{10}^{-31}}}{5\times {{10}^{4}}\times 1.6\times {{10}^{-19}}}}\] \[=2.99\times {{10}^{-19}}s\]
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