A) \[2.36 \times 1{{0}^{39}}\]
B) \[2.36 \times 1{{0}^{40}}\]
C) \[2.34 \times \,1{{0}^{41}}\]
D) \[2.34 \times 1{{0}^{42}}\]
Correct Answer: A
Solution :
Gravitational force \[{{F}_{G}}=\frac{G{{m}_{e}}{{m}_{p}}}{{{r}^{2}}}\] \[{{F}_{G}}= \frac{6.7\times 1{{0}^{-}}^{11}\times 9.1\times \,\,1{{0}^{-}}^{31}\times \,\,1.6\times {{10}^{-}}^{27}}{{{(5\times {{10}^{-11}})}^{2}}}\] \[=\,\,\,\,3.9\times {{10}^{-}}^{47}\,N\] Electrostatic force \[{{F}_{e}}=\frac{1}{4\pi {{\varepsilon }_{0}}}\frac{{{e}^{2}}}{{{r}^{2}}}\] \[{{F}_{e}}=\frac{9\times {{10}^{9}}\times 1.6\times {{10}^{-}}^{19}\times \,\,1.6\times {{10}^{-}}^{19}}{{{\left( 5\times {{10}^{-}}^{11} \right)}^{2}}}\] \[=\,\,\,9.22\times 1{{0}^{-\,8}}N\] So, \[\frac{{{F}_{e}}}{{{F}_{G}}}=\frac{9.22\times {{10}^{-8}}}{3.9\times {{10}^{-47}}}=2.36\times {{10}^{39}}\]
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