A) \[6.6\times {{10}^{39}}\]
B) \[2.4\times {{10}^{39}}\]
C) \[6.6\times {{10}^{29}}\]
D) \[2.4\times {{10}^{29}}\]
Correct Answer: B
Solution :
(b) \[2.4\times {{10}^{39}}\] For an electron and a proton: Electrostatic force, \[\left| {{F}_{e}} \right|=\frac{1}{4\pi {{\varepsilon }_{0}}}\frac{{{e}^{2}}}{{{r}^{2}}}\] Gravitational force, \[\left| {{F}_{g}} \right|=\frac{G{{m}_{e}}\,{{m}_{p}}}{{{r}^{2}}}\] \[\therefore \,\,\,\,\,\,\frac{\left| {{F}_{e}} \right|}{\left| {{F}_{g}} \right|}=\frac{1}{4\pi {{\varepsilon }_{0}}}\frac{{{e}^{2}}}{G{{m}_{e}}{{m}_{p}}}\] \[=\frac{9\times {{10}^{9}}\times {{\left( 1.6\times {{10}^{-19}} \right)}^{2}}}{6.67\times {{10}^{-11}}\times 9\times {{10}^{-31}}\times 1.66\times {{10}^{-27}}}\] \[=2.4\times {{10}^{39}}\]
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