A) \[{{10}^{-36}}\]
B) \[{{10}^{-39}}\]
C) \[{{10}^{-42}}\]
D) \[{{10}^{-47}}\]
Correct Answer: C
Solution :
The gravitational force between two electrons \[{{F}_{G}}=\frac{G{{m}^{2}}}{{{r}^{2}}}\] and electric force \[{{F}_{E}}=\frac{1}{4\pi {{\varepsilon }_{0}}}.\frac{{{e}^{2}}}{{{r}^{2}}}\] \[\therefore \] \[\frac{{{F}_{E}}}{{{F}_{G}}}=\frac{\frac{1}{4\pi {{\varepsilon }_{0}}}.\frac{{{e}^{2}}}{{{r}^{2}}}}{G{{m}^{2}}}\] \[=\frac{9\times {{10}^{9}}\times {{(1.6\times {{10}^{-19}})}^{2}}}{6.67\times {{10}^{-11}}\times {{(9.1\times {{10}^{-31}})}^{2}}}\] \[\approx {{10}^{42}}\] Or \[\frac{{{F}_{E}}}{{{F}_{G}}}={{10}^{-42}}\]
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